The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  0 X+1  1  0
 0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  0  X  0
 0  0  0  0  X  0  0  0  0  X  0  0  X  X  0  X  0  X  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  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+76x^12+16x^13+74x^14+96x^15+173x^16+240x^17+188x^18+320x^19+188x^20+240x^21+173x^22+96x^23+74x^24+16x^25+76x^26+1x^38

The gray image is a linear code over GF(2) with n=38, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0635 seconds.