The generator matrix

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

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+44x^12+220x^14+523x^16+776x^18+925x^20+864x^22+498x^24+184x^26+54x^28+4x^30+2x^32+1x^36

The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.258 seconds.