The generator matrix

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

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+183x^12+794x^14+1761x^16+3328x^18+4182x^20+3396x^22+1878x^24+656x^26+179x^28+18x^30+8x^32

The gray image is a linear code over GF(2) with n=40, k=14 and d=12.
This code was found by Heurico 1.16 in 6.77 seconds.