The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+27x^8+16x^9+50x^10+72x^11+49x^12+88x^13+54x^14+56x^15+48x^16+24x^17+22x^18+3x^20+2x^22

The gray image is a linear code over GF(2) with n=26, k=9 and d=8.
This code was found by Heurico 1.16 in 0.016 seconds.