The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  1  1  0  0  1  1
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  0 X+1  0  1 X+1  X
 0  0  1  0  1  1  0  1  0  1  1  0  0  1 X+1  X  0  0  X  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  0 X+1  1  1  X X+1  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  X  0  0  X  0  X  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  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+52x^12+106x^13+208x^14+304x^15+439x^16+640x^17+816x^18+992x^19+1061x^20+980x^21+816x^22+688x^23+450x^24+304x^25+208x^26+64x^27+38x^28+18x^29+6x^32+1x^36

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 0.971 seconds.