The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 2 1 X X 1 1 1
0 X 0 X 0 0 X X+2 0 2 2 X X 0 X+2 X X X+2 0
0 0 X X 0 X+2 X 0 2 X X X X 0 0 X+2 X X 0
0 0 0 2 0 0 0 2 2 2 2 0 0 2 0 0 2 0 0
0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 2 0 2
0 0 0 0 0 2 0 0 0 2 0 2 2 0 2 0 2 0 2
0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 0 0 2
generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+22x^13+47x^14+70x^15+193x^16+102x^17+526x^18+118x^19+540x^20+114x^21+184x^22+66x^23+30x^24+18x^25+10x^26+2x^27+4x^28+1x^30
The gray image is a code over GF(2) with n=76, k=11 and d=26.
This code was found by Heurico 1.16 in 0.145 seconds.