The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  0  0  0  0  1  X  1  X
 0  1  0  0  0  1  1  1  X  0 X+1  1  1  1  1  X  1  1  1  1
 0  0  1  0  1  1  0  1  0 X+1  1  X  1  X  1  1  1  X  0  X
 0  0  0  1  1  0  1 X+1  1  X X+1  0  X  1  X X+1  1  0  1  0
 0  0  0  0  X  0  0  X  0  X  X  X  0  0  0  X  X  X  X  X
 0  0  0  0  0  X  0  0  X  X  X  0  0  X  X  0  X  0  0  X
 0  0  0  0  0  0  X  0  X  X  0  X  0  0  X  X  X  0  0  0

generates a code of length 20 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+62x^14+102x^15+150x^16+184x^17+191x^18+206x^19+219x^20+256x^21+203x^22+194x^23+131x^24+72x^25+53x^26+10x^27+9x^28+3x^30+2x^32

The gray image is a linear code over GF(2) with n=40, k=11 and d=14.
This code was found by Heurico 1.16 in 0.118 seconds.