The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1
0 1 1 0 1 1 0 1 1 0 X+1 1 0 0 X+1 X 0
0 0 X 0 0 0 0 0 0 0 X X X 0 0 X 0
0 0 0 X 0 0 0 0 0 X X X 0 X 0 0 0
0 0 0 0 X 0 0 0 X X 0 0 X X X X 0
0 0 0 0 0 X 0 0 X X X X X X 0 X X
0 0 0 0 0 0 X 0 X 0 X 0 X X 0 0 X
0 0 0 0 0 0 0 X X X 0 X 0 0 X X 0
generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+14x^10+14x^11+39x^12+54x^13+82x^14+110x^15+123x^16+150x^17+118x^18+122x^19+80x^20+50x^21+38x^22+10x^23+12x^24+2x^25+4x^26+1x^28
The gray image is a linear code over GF(2) with n=34, k=10 and d=10.
This code was found by Heurico 1.16 in 0.0128 seconds.