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.