The generator matrix

1 0 0 0 0 0 1 1 1 1 0 1 X 1 1 X X 1 1 1
0 1 0 0 0 0 0 0 1 1 1 X 0 X+1 X 1 1 0 1 0
0 0 1 0 0 0 0 1 0 X 0 X+1 1 1 0 X X+1 X 0 0
0 0 0 1 0 0 0 1 1 0 X+1 X+1 X+1 X 1 1 X+1 1 0 0
0 0 0 0 1 0 1 0 X+1 X 1 X X 0 X 0 X+1 X+1 0 0
0 0 0 0 0 1 1 X+1 X X+1 X+1 0 0 X+1 X 0 1 1 0 0
0 0 0 0 0 0 X X 0 X X 0 X 0 X X 0 X 0 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+112x^12+94x^13+284x^14+294x^15+453x^16+620x^17+674x^18+1020x^19+928x^20+1048x^21+790x^22+664x^23+554x^24+276x^25+222x^26+68x^27+64x^28+10x^29+14x^30+2x^31

The gray image is a linear code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.10 in 0.406 seconds.