The generator matrix

1 0 0 0 0 0 1 1 1 0 1 1 X X 1 1 X X 1 1
0 1 0 0 0 0 0 1 1 X 0 X+1 1 1 X+1 X+1 X 0 0 0
0 0 1 0 0 0 1 0 X 1 X+1 X X 0 X+1 X+1 1 1 0 0
0 0 0 1 0 0 1 X X+1 X X+1 X 1 X X 0 X+1 0 0 0
0 0 0 0 1 0 1 X+1 0 1 X 0 1 1 X+1 X+1 1 X+1 0 0
0 0 0 0 0 1 X 1 X 1 X+1 0 0 1 X 1 1 1 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+49x^12+220x^14+493x^16+792x^18+975x^20+810x^22+513x^24+180x^26+48x^28+14x^30+1x^32

The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.10 in 0.109 seconds.