The generator matrix

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

generates a code of length 19 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+42x^13+123x^14+142x^15+171x^16+192x^17+201x^18+256x^19+248x^20+238x^21+173x^22+110x^23+88x^24+36x^25+15x^26+4x^27+4x^28+4x^29

The gray image is a linear code over GF(2) with n=38, k=11 and d=13.
This code was found by Heurico 1.10 in 0.031 seconds.