The generator matrix

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

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+782x^14+1770x^16+3372x^18+4138x^20+3360x^22+1932x^24+644x^26+167x^28+34x^30+1x^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 22.2 seconds.