The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  0  1  0  1  1  1  0  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  X  1 X+1  1  1  1  1  1
 0  0  1  0  0  0  0  0 X+1  0  1  1  1 X+1  X  X X+1  0 X+1  1
 0  0  0  1  0  0  0  1  1  1  0  X  0  1  1 X+1 X+1  X  X  X
 0  0  0  0  1  0  1  1  0  1  0  X X+1  X  X  1  1 X+1  X  0
 0  0  0  0  0  1  1  0 X+1  1  X  X  0  1 X+1  0 X+1  1  0  X
 0  0  0  0  0  0  X  0  X  0  0  X  X  X  0  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  0  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+142x^12+164x^13+455x^14+556x^15+955x^16+1204x^17+1541x^18+2156x^19+1932x^20+2172x^21+1662x^22+1252x^23+954x^24+540x^25+410x^26+132x^27+110x^28+16x^29+27x^30+2x^32+1x^34

The gray image is a linear code over GF(2) with n=40, k=14 and d=12.
This code was found by Heurico 1.16 in 8.55 seconds.