The generator matrix

 1  0  0  1  1  1  0  1  1  0  1  0  1  X  X  1  1  0  0
 0  1  0  1  0  1  1  0  0  X  1  1 X+1  1  1 X+1  X  0  0
 0  0  1  1  1  0  1  0  1  1  1  X  0 X+1  1  0  1  1  1
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  0  0  X
 0  0  0  0  X  0  0  0  0  X  X  0  X  0  0  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X
 0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  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+109x^12+272x^14+683x^16+912x^18+1146x^20+560x^22+338x^24+48x^26+25x^28+2x^32

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 0.243 seconds.