The generator matrix

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

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+92x^13+177x^14+254x^15+317x^16+360x^17+468x^18+594x^19+494x^20+444x^21+326x^22+226x^23+146x^24+64x^25+52x^26+14x^27+13x^28+1x^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 10.7 seconds.