The generator matrix

 1  0  0  0  0  0  1  1  1  1  X  0  1  0  1  0  X  0  1  1
 0  1  0  0  0  0  0  0 X+1  X  0  1 X+1  1  0  X  1  X  X  0
 0  0  1  0  0  0  0 X+1  1  X  1  0  X  1 X+1  1  0  1  0  0
 0  0  0  1  0  0  0  1  0  1  1  X  0  1  X X+1  1  0 X+1  0
 0  0  0  0  1  0  1  0  1 X+1  1  X X+1  0 X+1  0  1  1 X+1  0
 0  0  0  0  0  1  1 X+1  X  X X+1 X+1  X  X X+1  0 X+1  0  1  0
 0  0  0  0  0  0  X  X  0  0  X  X  X  X  0  X  0  0  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+94x^12+84x^13+273x^14+326x^15+463x^16+598x^17+747x^18+990x^19+917x^20+1094x^21+789x^22+658x^23+475x^24+258x^25+225x^26+74x^27+97x^28+14x^29+14x^30+1x^32

The gray image is a linear code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.16 in 1.2 seconds.