The generator matrix

 1  0  0  0  0  1  1  1  1  X  1  1  X  X  1  X  1  1  1
 0  1  0  0  0  0  0 X+1  1  1  X  1  1  1  0  X  1  0  0
 0  0  1  0  0  0  1  1  0 X+1 X+1  X  1 X+1  0  1  1  1  0
 0  0  0  1  0  1  1  0 X+1  1  0 X+1  X X+1  1  1 X+1  0  0
 0  0  0  0  1  1  0 X+1  X X+1  1 X+1  1  X  X  X  1  X  0
 0  0  0  0  0  X  0  X  0  X  X  X  0  X  X  X  0  0  0
 0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  X  0  0  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+82x^12+98x^13+204x^14+226x^15+326x^16+408x^17+397x^18+562x^19+425x^20+444x^21+357x^22+230x^23+173x^24+72x^25+63x^26+6x^27+17x^28+2x^29+3x^30

The gray image is a linear code over GF(2) with n=38, k=12 and d=12.
This code was found by Heurico 1.16 in 0.283 seconds.