The generator matrix
1 0 0 0 0 0 0 0 1 1 1 1 1 X 0 0 1 1 1
0 1 0 0 0 0 0 0 0 1 1 X 1 1 X X 1 0 0
0 0 1 0 0 0 0 0 1 0 0 1 X+1 X 1 1 X X 0
0 0 0 1 0 0 0 0 1 1 X+1 0 0 1 X 1 1 0 0
0 0 0 0 1 0 0 0 1 X 1 X X+1 0 1 X+1 X+1 X 0
0 0 0 0 0 1 0 0 1 X+1 X 1 0 0 X+1 0 1 X+1 0
0 0 0 0 0 0 1 0 X 1 0 X+1 X+1 1 1 X+1 0 X+1 0
0 0 0 0 0 0 0 1 X 1 X+1 1 X 1 1 X X X+1 0
generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+50x^9+181x^10+456x^11+861x^12+1404x^13+2379x^14+3750x^15+5297x^16+6780x^17+7690x^18+7992x^19+7594x^20+6544x^21+5326x^22+3844x^23+2462x^24+1538x^25+785x^26+336x^27+169x^28+68x^29+23x^30+6x^31
The gray image is a linear code over GF(2) with n=38, k=16 and d=9.
This code was found by Heurico 1.11 in 11.6 seconds.