The generator matrix

 1  0  0  0  0  1  1  1  X  X  1  0  X  1  1  1  X  0  0  1
 0  1  0  0  0  0  0  0  1  1  1  1  X X+1  X  X  X  1  1  0
 0  0  1  0  0  0  1  1  1  0  0  X  X  1  0 X+1  1  1  0  0
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  1  0  X  1  X  0  0  0
 0  0  0  0  1  1  0  1  1  1  0 X+1 X+1 X+1  1  1  1  1  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  X  X  0  0  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  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+95x^12+90x^13+241x^14+312x^15+545x^16+598x^17+710x^18+1006x^19+860x^20+1098x^21+824x^22+638x^23+484x^24+258x^25+250x^26+90x^27+61x^28+4x^29+23x^30+2x^31+2x^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 1.08 seconds.