The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 X 1 1 1
0 1 1 0 1 1 0 1 1 0 X+1 1 0 X+1 1 0 0 X 0
0 0 X 0 0 0 0 0 0 0 X X 0 0 X 0 X X 0
0 0 0 X 0 0 0 0 0 X X X 0 X 0 X X 0 0
0 0 0 0 X 0 0 0 X X 0 0 0 0 0 X X X 0
0 0 0 0 0 X 0 0 X X X X X 0 0 0 X X 0
0 0 0 0 0 0 X 0 X 0 X 0 0 X X X X 0 0
0 0 0 0 0 0 0 X X X 0 X 0 X X 0 X X 0
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+25x^12+8x^13+67x^14+48x^15+77x^16+120x^17+89x^18+160x^19+86x^20+120x^21+74x^22+48x^23+66x^24+8x^25+22x^26+1x^28+3x^30+1x^34
The gray image is a linear code over GF(2) with n=38, k=10 and d=12.
This code was found by Heurico 1.16 in 0.019 seconds.