Optimal:
"A32BO2" → 0; "BPWDH8" → 1; "IYIH94" → 2; "AMSAKO" → 3; "N7OKDZ" → 4; "DJQ16O" → 5; "WWVK21" → 6; "JKR7ZR" → 7; "DBIOC9" → 8; "QG2CBR" → 9; "HM02MI" → 10; "B21KES" → 11; "F3D3D4" → 12; "CF2RHU" → 13; "Q0WQSH" → 14; "EYBSWV" → 15; "K7FONH" → 16; "JP7A43" → 17; "ILMJRU" → 18

No collisions, 2 unused cells in the hash table:
(39a+26b+46c+30d+7e+45f) (mod 21)
(68a+5b+31c+68d+60e+73f) (mod 21)
(39a+58b+4c+17d+34e+9f) (mod 21)

No collisions, 1 unused cell in the hash table:
It takes less than 1 second to generate one of these.
(60a+52b+6c+9d+4e+23f) (mod 20)
(28a+16b+50c+35d+66e+23f) (mod 20)
(20a+48b+14c+31d+76e+37f) (mod 20)
(40a+48b+34c+21d+56e+27f) (mod 20)
(60a+36b+78c+47d+52e+69f) (mod 20)

Only 1 collision:
(18a+54b+69c+29d+6e+60f) (mod 18)
(17a+66b+49c+63d+1e+35f) (mod 18)
(59a+30b+55c+39d+25e+41f) (mod 18)
(13a+6b+17c+69d+47e+13f) (mod 18)
(0a+51b+43c+42d+58e+69f) (mod 18)
(79a+47b+63c+69d+39e+39f) (mod 18)

Finding 4 solutions in 2 minutes:
Solution: (550a+930b+455c+189d+93e+371f) (mod 976) (mod 19)
A32BO2 → 0; N7OKDZ → 1; JKR7ZR → 2; F3D3D4 → 3; IYIH94 → 4; BPWDH8 → 5; DJQ16O → 6; EYBSWV → 7; DBIOC9 → 8; K7FONH → 9; ILMJRU → 10; CF2RHU → 11; AMSAKO → 12; HM02MI → 13; QG2CBR → 14; Q0WQSH → 15; JP7A43 → 16; B21KES → 17; WWVK21 → 18; 
Solution: (899a+938b+42c+153d+908e+143f) (mod 241) (mod 19)
A32BO2 → 0; DJQ16O → 1; Q0WQSH → 2; B21KES → 3; WWVK21 → 4; DBIOC9 → 5; ILMJRU → 6; CF2RHU → 7; BPWDH8 → 8; EYBSWV → 9; HM02MI → 10; IYIH94 → 11; JP7A43 → 12; N7OKDZ → 13; K7FONH → 14; QG2CBR → 15; JKR7ZR → 16; F3D3D4 → 17; AMSAKO → 18; 
Tested 100000000 random combinations.
Solution: (709a+979b+79c+293d+29e+102f) (mod 682) (mod 19)
QG2CBR → 0; EYBSWV → 1; BPWDH8 → 2; CF2RHU → 3; ILMJRU → 4; JKR7ZR → 5; F3D3D4 → 6; Q0WQSH → 7; DJQ16O → 8; N7OKDZ → 9; HM02MI → 10; B21KES → 11; K7FONH → 12; AMSAKO → 13; JP7A43 → 14; A32BO2 → 15; IYIH94 → 16; DBIOC9 → 17; WWVK21 → 18; 
Done. Found 3 solutions after 113338171 iterations.
Solution: (704a+554b+219c+3d+245e+337f) (mod 310) (mod 19)
Q0WQSH → 0; ILMJRU → 1; HM02MI → 2; JKR7ZR → 3; N7OKDZ → 4; IYIH94 → 5; CF2RHU → 6; A32BO2 → 7; BPWDH8 → 8; F3D3D4 → 9; DJQ16O → 10; AMSAKO → 11; EYBSWV → 12; JP7A43 → 13; B21KES → 14; WWVK21 → 15; QG2CBR → 16; K7FONH → 17; DBIOC9 → 18; 
BUILD SUCCESSFUL (total time: 1 minute 55 seconds)

Finding 30 solutions in 12 minutes:
Solution: (14a+72b+859c+89d+517e+660f) (mod 767) (mod 19)
JKR7ZR → 0; EYBSWV → 1; HM02MI → 2; DJQ16O → 3; DBIOC9 → 4; IYIH94 → 5; AMSAKO → 6; F3D3D4 → 7; ILMJRU → 8; QG2CBR → 9; N7OKDZ → 10; JP7A43 → 11; B21KES → 12; BPWDH8 → 13; WWVK21 → 14; K7FONH → 15; CF2RHU → 16; A32BO2 → 17; Q0WQSH → 18; 
Solution: (242a+454b+675c+732d+486e+685f) (mod 312) (mod 19)
K7FONH → 0; DJQ16O → 1; A32BO2 → 2; JP7A43 → 3; EYBSWV → 4; HM02MI → 5; Q0WQSH → 6; AMSAKO → 7; N7OKDZ → 8; BPWDH8 → 9; ILMJRU → 10; JKR7ZR → 11; CF2RHU → 12; IYIH94 → 13; B21KES → 14; QG2CBR → 15; WWVK21 → 16; DBIOC9 → 17; F3D3D4 → 18; 
Solution: (701a+407b+562c+707d+539e+946f) (mod 724) (mod 19)
CF2RHU → 0; DBIOC9 → 1; N7OKDZ → 2; EYBSWV → 3; Q0WQSH → 4; A32BO2 → 5; AMSAKO → 6; JP7A43 → 7; DJQ16O → 8; IYIH94 → 9; JKR7ZR → 10; B21KES → 11; WWVK21 → 12; HM02MI → 13; QG2CBR → 14; F3D3D4 → 15; K7FONH → 16; ILMJRU → 17; BPWDH8 → 18; 
Solution: (747a+732b+975c+316d+767e+701f) (mod 538) (mod 19)
DJQ16O → 0; BPWDH8 → 1; JP7A43 → 2; ILMJRU → 3; Q0WQSH → 4; CF2RHU → 5; K7FONH → 6; EYBSWV → 7; DBIOC9 → 8; WWVK21 → 9; QG2CBR → 10; JKR7ZR → 11; IYIH94 → 12; HM02MI → 13; N7OKDZ → 14; B21KES → 15; A32BO2 → 16; F3D3D4 → 17; AMSAKO → 18; 
Solution: (782a+940b+801c+267d+835e+405f) (mod 327) (mod 19)
JP7A43 → 0; F3D3D4 → 1; QG2CBR → 2; HM02MI → 3; DBIOC9 → 4; AMSAKO → 5; K7FONH → 6; CF2RHU → 7; B21KES → 8; JKR7ZR → 9; EYBSWV → 10; IYIH94 → 11; A32BO2 → 12; BPWDH8 → 13; N7OKDZ → 14; DJQ16O → 15; ILMJRU → 16; Q0WQSH → 17; WWVK21 → 18; 
Solution: (5a+525b+65c+431d+104e+802f) (mod 175) (mod 19)
IYIH94 → 0; A32BO2 → 1; F3D3D4 → 2; DBIOC9 → 3; EYBSWV → 4; JP7A43 → 5; HM02MI → 6; BPWDH8 → 7; N7OKDZ → 8; JKR7ZR → 9; CF2RHU → 10; AMSAKO → 11; QG2CBR → 12; B21KES → 13; Q0WQSH → 14; K7FONH → 15; DJQ16O → 16; WWVK21 → 17; ILMJRU → 18; 
Tested 100000000 random combinations.
Solution: (690a+932b+172c+533d+847e+199f) (mod 848) (mod 19)
WWVK21 → 0; BPWDH8 → 1; DBIOC9 → 2; HM02MI → 3; IYIH94 → 4; QG2CBR → 5; Q0WQSH → 6; JP7A43 → 7; EYBSWV → 8; ILMJRU → 9; N7OKDZ → 10; CF2RHU → 11; JKR7ZR → 12; A32BO2 → 13; K7FONH → 14; B21KES → 15; AMSAKO → 16; F3D3D4 → 17; DJQ16O → 18; 
Solution: (154a+505b+49c+170d+304e+66f) (mod 158) (mod 19)
ILMJRU → 0; B21KES → 1; AMSAKO → 2; IYIH94 → 3; K7FONH → 4; Q0WQSH → 5; N7OKDZ → 6; A32BO2 → 7; CF2RHU → 8; JP7A43 → 9; BPWDH8 → 10; DBIOC9 → 11; JKR7ZR → 12; EYBSWV → 13; F3D3D4 → 14; DJQ16O → 15; QG2CBR → 16; HM02MI → 17; WWVK21 → 18; 
Solution: (753a+377b+866c+734d+226e+65f) (mod 214) (mod 19)
K7FONH → 0; A32BO2 → 1; N7OKDZ → 2; JP7A43 → 3; QG2CBR → 4; DJQ16O → 5; AMSAKO → 6; WWVK21 → 7; IYIH94 → 8; EYBSWV → 9; ILMJRU → 10; B21KES → 11; DBIOC9 → 12; HM02MI → 13; F3D3D4 → 14; JKR7ZR → 15; CF2RHU → 16; Q0WQSH → 17; BPWDH8 → 18; 
Solution: (422a+104b+103c+864d+707e+44f) (mod 29) (mod 19)
CF2RHU → 0; QG2CBR → 1; ILMJRU → 2; DBIOC9 → 3; HM02MI → 4; EYBSWV → 5; DJQ16O → 6; N7OKDZ → 7; IYIH94 → 8; BPWDH8 → 9; Q0WQSH → 10; A32BO2 → 11; B21KES → 12; WWVK21 → 13; JP7A43 → 14; JKR7ZR → 15; K7FONH → 16; AMSAKO → 17; F3D3D4 → 18; 
Solution: (405a+4b+537c+235d+452e+487f) (mod 544) (mod 19)
HM02MI → 0; JKR7ZR → 1; ILMJRU → 2; EYBSWV → 3; IYIH94 → 4; WWVK21 → 5; N7OKDZ → 6; DJQ16O → 7; QG2CBR → 8; B21KES → 9; AMSAKO → 10; JP7A43 → 11; Q0WQSH → 12; A32BO2 → 13; K7FONH → 14; CF2RHU → 15; F3D3D4 → 16; BPWDH8 → 17; DBIOC9 → 18; 
Tested 200000000 random combinations.
Solution: (857a+567b+630c+914d+909e+448f) (mod 541) (mod 19)
F3D3D4 → 0; K7FONH → 1; HM02MI → 2; ILMJRU → 3; Q0WQSH → 4; DJQ16O → 5; QG2CBR → 6; BPWDH8 → 7; EYBSWV → 8; B21KES → 9; JP7A43 → 10; WWVK21 → 11; N7OKDZ → 12; AMSAKO → 13; DBIOC9 → 14; CF2RHU → 15; A32BO2 → 16; JKR7ZR → 17; IYIH94 → 18; 
Solution: (44a+147b+424c+157d+403e+664f) (mod 81) (mod 19)
JP7A43 → 0; JKR7ZR → 1; EYBSWV → 2; Q0WQSH → 3; IYIH94 → 4; N7OKDZ → 5; WWVK21 → 6; DBIOC9 → 7; CF2RHU → 8; HM02MI → 9; AMSAKO → 10; ILMJRU → 11; QG2CBR → 12; K7FONH → 13; F3D3D4 → 14; DJQ16O → 15; B21KES → 16; BPWDH8 → 17; A32BO2 → 18; 
Solution: (594a+882b+610c+148d+53e+352f) (mod 733) (mod 19)
Q0WQSH → 0; DJQ16O → 1; QG2CBR → 2; BPWDH8 → 3; EYBSWV → 4; B21KES → 5; HM02MI → 6; JKR7ZR → 7; ILMJRU → 8; JP7A43 → 9; IYIH94 → 10; WWVK21 → 11; A32BO2 → 12; K7FONH → 13; CF2RHU → 14; F3D3D4 → 15; AMSAKO → 16; DBIOC9 → 17; N7OKDZ → 18; 
Solution: (95a+826b+173c+124d+756e+210f) (mod 826) (mod 19)
A32BO2 → 0; AMSAKO → 1; JKR7ZR → 2; B21KES → 3; N7OKDZ → 4; HM02MI → 5; QG2CBR → 6; K7FONH → 7; EYBSWV → 8; DJQ16O → 9; BPWDH8 → 10; F3D3D4 → 11; Q0WQSH → 12; WWVK21 → 13; ILMJRU → 14; DBIOC9 → 15; IYIH94 → 16; CF2RHU → 17; JP7A43 → 18; 
Solution: (501a+913b+736c+580d+397e+412f) (mod 5) (mod 19)
N7OKDZ → 0; A32BO2 → 1; ILMJRU → 2; DBIOC9 → 3; BPWDH8 → 4; WWVK21 → 5; K7FONH → 6; B21KES → 7; EYBSWV → 8; DJQ16O → 9; HM02MI → 10; JP7A43 → 11; JKR7ZR → 12; AMSAKO → 13; QG2CBR → 14; Q0WQSH → 15; F3D3D4 → 16; IYIH94 → 17; CF2RHU → 18; 
Solution: (381a+395b+206c+733d+359e+248f) (mod 173) (mod 19)
Q0WQSH → 0; EYBSWV → 1; BPWDH8 → 2; QG2CBR → 3; AMSAKO → 4; IYIH94 → 5; A32BO2 → 6; K7FONH → 7; WWVK21 → 8; DBIOC9 → 9; N7OKDZ → 10; DJQ16O → 11; JKR7ZR → 12; HM02MI → 13; F3D3D4 → 14; CF2RHU → 15; ILMJRU → 16; B21KES → 17; JP7A43 → 18; 
Solution: (481a+29b+482c+303d+490e+503f) (mod 290) (mod 19)
HM02MI → 0; Q0WQSH → 1; DBIOC9 → 2; JP7A43 → 3; F3D3D4 → 4; N7OKDZ → 5; EYBSWV → 6; JKR7ZR → 7; QG2CBR → 8; AMSAKO → 9; A32BO2 → 10; CF2RHU → 11; ILMJRU → 12; IYIH94 → 13; WWVK21 → 14; BPWDH8 → 15; DJQ16O → 16; K7FONH → 17; B21KES → 18; 
Tested 300000000 random combinations.
Solution: (768a+154b+580c+135d+279e+332f) (mod 699) (mod 19)
HM02MI → 0; CF2RHU → 1; JKR7ZR → 2; QG2CBR → 3; IYIH94 → 4; EYBSWV → 5; DJQ16O → 6; JP7A43 → 7; F3D3D4 → 8; B21KES → 9; N7OKDZ → 10; K7FONH → 11; ILMJRU → 12; Q0WQSH → 13; WWVK21 → 14; A32BO2 → 15; AMSAKO → 16; DBIOC9 → 17; BPWDH8 → 18; 
Solution: (518a+591b+493c+622d+534e+556f) (mod 560) (mod 19)
WWVK21 → 0; N7OKDZ → 1; IYIH94 → 2; AMSAKO → 3; JP7A43 → 4; DBIOC9 → 5; EYBSWV → 6; QG2CBR → 7; CF2RHU → 8; F3D3D4 → 9; B21KES → 10; K7FONH → 11; Q0WQSH → 12; HM02MI → 13; BPWDH8 → 14; ILMJRU → 15; JKR7ZR → 16; DJQ16O → 17; A32BO2 → 18; 
Solution: (972a+386b+519c+686d+443e+610f) (mod 107) (mod 19)
QG2CBR → 0; N7OKDZ → 1; IYIH94 → 2; BPWDH8 → 3; WWVK21 → 4; JP7A43 → 5; AMSAKO → 6; DJQ16O → 7; K7FONH → 8; Q0WQSH → 9; HM02MI → 10; EYBSWV → 11; F3D3D4 → 12; ILMJRU → 13; JKR7ZR → 14; CF2RHU → 15; A32BO2 → 16; B21KES → 17; DBIOC9 → 18; 
Solution: (66a+377b+83c+377d+735e+980f) (mod 863) (mod 19)
QG2CBR → 0; Q0WQSH → 1; A32BO2 → 2; HM02MI → 3; B21KES → 4; DJQ16O → 5; F3D3D4 → 6; AMSAKO → 7; IYIH94 → 8; BPWDH8 → 9; WWVK21 → 10; EYBSWV → 11; K7FONH → 12; JKR7ZR → 13; JP7A43 → 14; CF2RHU → 15; ILMJRU → 16; DBIOC9 → 17; N7OKDZ → 18; 
Solution: (816a+411b+87c+978d+757e+705f) (mod 567) (mod 19)
Q0WQSH → 0; B21KES → 1; N7OKDZ → 2; IYIH94 → 3; AMSAKO → 4; CF2RHU → 5; WWVK21 → 6; BPWDH8 → 7; EYBSWV → 8; HM02MI → 9; JP7A43 → 10; DJQ16O → 11; JKR7ZR → 12; A32BO2 → 13; F3D3D4 → 14; DBIOC9 → 15; QG2CBR → 16; K7FONH → 17; ILMJRU → 18; 
Solution: (866a+43b+921c+0d+422e+310f) (mod 793) (mod 19)
B21KES → 0; A32BO2 → 1; JKR7ZR → 2; BPWDH8 → 3; QG2CBR → 4; JP7A43 → 5; F3D3D4 → 6; DJQ16O → 7; HM02MI → 8; K7FONH → 9; EYBSWV → 10; WWVK21 → 11; ILMJRU → 12; IYIH94 → 13; AMSAKO → 14; Q0WQSH → 15; N7OKDZ → 16; CF2RHU → 17; DBIOC9 → 18; 
Tested 400000000 random combinations.
Solution: (126a+208b+625c+509d+165e+976f) (mod 532) (mod 19)
IYIH94 → 0; QG2CBR → 1; JP7A43 → 2; K7FONH → 3; DBIOC9 → 4; DJQ16O → 5; BPWDH8 → 6; Q0WQSH → 7; B21KES → 8; EYBSWV → 9; CF2RHU → 10; A32BO2 → 11; N7OKDZ → 12; HM02MI → 13; F3D3D4 → 14; WWVK21 → 15; ILMJRU → 16; JKR7ZR → 17; AMSAKO → 18; 
Solution: (288a+492b+640c+178d+688e+392f) (mod 127) (mod 19)
ILMJRU → 0; EYBSWV → 1; JKR7ZR → 2; A32BO2 → 3; CF2RHU → 4; K7FONH → 5; N7OKDZ → 6; F3D3D4 → 7; DJQ16O → 8; JP7A43 → 9; BPWDH8 → 10; WWVK21 → 11; Q0WQSH → 12; B21KES → 13; QG2CBR → 14; IYIH94 → 15; AMSAKO → 16; DBIOC9 → 17; HM02MI → 18; 
Solution: (830a+447b+859c+222d+42e+41f) (mod 966) (mod 19)
B21KES → 0; JP7A43 → 1; HM02MI → 2; QG2CBR → 3; A32BO2 → 4; WWVK21 → 5; F3D3D4 → 6; DBIOC9 → 7; DJQ16O → 8; ILMJRU → 9; IYIH94 → 10; K7FONH → 11; EYBSWV → 12; N7OKDZ → 13; Q0WQSH → 14; AMSAKO → 15; CF2RHU → 16; BPWDH8 → 17; JKR7ZR → 18; 
Solution: (772a+643b+255c+962d+732e+947f) (mod 50) (mod 19)
WWVK21 → 0; Q0WQSH → 1; DJQ16O → 2; F3D3D4 → 3; IYIH94 → 4; QG2CBR → 5; A32BO2 → 6; DBIOC9 → 7; HM02MI → 8; B21KES → 9; CF2RHU → 10; K7FONH → 11; BPWDH8 → 12; AMSAKO → 13; JKR7ZR → 14; N7OKDZ → 15; ILMJRU → 16; EYBSWV → 17; JP7A43 → 18; 
Solution: (325a+77b+494c+152d+976e+308f) (mod 326) (mod 19)
AMSAKO → 0; IYIH94 → 1; A32BO2 → 2; Q0WQSH → 3; HM02MI → 4; ILMJRU → 5; BPWDH8 → 6; JKR7ZR → 7; EYBSWV → 8; F3D3D4 → 9; JP7A43 → 10; WWVK21 → 11; CF2RHU → 12; K7FONH → 13; QG2CBR → 14; DJQ16O → 15; N7OKDZ → 16; DBIOC9 → 17; B21KES → 18; 
Tested 500000000 random combinations.
Solution: (552a+854b+857c+426d+886e+262f) (mod 145) (mod 19)
ILMJRU → 0; K7FONH → 1; CF2RHU → 2; IYIH94 → 3; HM02MI → 4; DJQ16O → 5; A32BO2 → 6; DBIOC9 → 7; N7OKDZ → 8; BPWDH8 → 9; JP7A43 → 10; AMSAKO → 11; Q0WQSH → 12; B21KES → 13; EYBSWV → 14; JKR7ZR → 15; WWVK21 → 16; F3D3D4 → 17; QG2CBR → 18; 
Done. Found 30 solutions after 520563179 iterations.
BUILD SUCCESSFUL (total time: 11 minutes 56 seconds)

--Daniel "3ICE" Berezvai