The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 0 1 1 0
0 1 0 1 0 1 1 0 0 1 X+1 1 1 0 X 1 1
0 0 1 1 1 0 1 0 1 1 0 X 1 1 1 1 0
0 0 0 X 0 0 0 0 0 0 0 X 0 X X 0 X
0 0 0 0 X 0 0 0 0 0 0 X X 0 X X X
0 0 0 0 0 X 0 0 0 0 X 0 X X 0 0 X
0 0 0 0 0 0 X 0 0 X X X 0 X X 0 0
0 0 0 0 0 0 0 X 0 X 0 X 0 0 0 X X
0 0 0 0 0 0 0 0 X X X 0 X 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+70x^10+272x^12+648x^14+1057x^16+1057x^18+648x^20+272x^22+70x^24+1x^34
The gray image is a linear code over GF(2) with n=34, k=12 and d=10.
This code was found by Heurico 1.16 in 67.1 seconds.