The generator matrix
1 1 1 1 1 1 1 1 X X 1 1 2 2 1 X 2 1 1
0 X 0 0 0 X X+2 X 2 0 X 0 X X X X+2 X 0 0
0 0 X 0 X X X+2 0 0 X X X X+2 2 0 X X+2 2 0
0 0 0 X X 0 X+2 X X X 0 X+2 2 X+2 X+2 X+2 0 0 0
0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 0
0 0 0 0 0 2 0 0 2 2 0 2 2 0 2 2 2 0 0
0 0 0 0 0 0 2 0 2 2 2 0 2 2 0 2 2 0 0
0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 2 0
generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+104x^12+78x^13+219x^14+234x^15+727x^16+422x^17+2015x^18+562x^19+2014x^20+458x^21+760x^22+222x^23+216x^24+66x^25+72x^26+6x^27+10x^28+5x^30+1x^34
The gray image is a code over GF(2) with n=76, k=13 and d=24.
This code was found by Heurico 1.16 in 0.603 seconds.