The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  0  X  1  0  1  0
 0  1  0  0  0  1  1  1  X  0 X+1  1  1  1  0  1  1  X  1
 0  0  1  0  1  1  0  1  0 X+1  1  1  X  0  1  X  X  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  X  1  0 X+1  1  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  0  X  0  0
 0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  0  X  0
 0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  0  X  X  0
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  0  X  X  0  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+76x^12+82x^13+154x^14+222x^15+313x^16+434x^17+485x^18+558x^19+464x^20+454x^21+332x^22+234x^23+158x^24+54x^25+50x^26+10x^27+12x^28+2x^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 Heurico 1.16 in 0.272 seconds.