The generator matrix

1 1 X 0 1 1 0 0 1 X 1 0 1 1 1 1 1 1 1
0 X 1 1 0 0 1 1 X+1 X X+1 0 1 1 X X+1 X+1 0 0
1 X 1 0 0 X+1 1 X X 1 X 0 X+1 X 1 X+1 X+1 X+1 0
0 0 0 X X+1 1 X+1 X+1 X+1 0 0 1 X+1 1 0 X+1 X 1 0
0 0 0 0 0 0 X X X+1 X+1 X+1 1 X+1 0 1 X 1 X+1 0
0 0 0 0 0 0 0 0 0 X 0 X X+1 1 1 X+1 X+1 X+1 X

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+53x^12+102x^13+184x^14+234x^15+334x^16+386x^17+400x^18+550x^19+535x^20+474x^21+331x^22+230x^23+157x^24+62x^25+43x^26+10x^27+8x^28+1x^30+1x^34

The gray image is a linear code over GF(2) with n=38, k=12 and d=12.
This code was found by an older version of Heurico in 0 seconds.