The generator matrix

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

generates a code of length 17 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+32x^13+16x^14+62x^16+64x^17+32x^18+32x^21+16x^22+1x^32

The gray image is a linear code over GF(2) with n=34, k=8 and d=13.
This code was found by Heurico 1.16 in 2.62 seconds.