The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  X  0  1  0  X  0  1  1
 0  1  0  1  0  1  1  0  X  1  1  1  0 X+1  0  X  1  0  1
 0  0  1  1  1  0  1  0  1 X+1  0  1  1 X+1  1  1  0  0  1
 0  0  0  X  0  0  0  0  0  X  X  X  0  0  X  X  0  0  0
 0  0  0  0  X  0  0  0  X  0  X  X  X  0  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  X  0  X  0  X  0  X
 0  0  0  0  0  0  0  X  X  X  X  0  0  X  0  X  X  X  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+36x^12+170x^14+328x^16+482x^18+490x^20+350x^22+158x^24+22x^26+10x^28+1x^32

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 0.0638 seconds.