The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1
 0  1  1  0  1  1  0 X+1  1  X  1  1  0
 0  0  X  0  0  0  0  0  X  0  X  X  0
 0  0  0  X  0  0  0  0  X  X  0  X  0
 0  0  0  0  X  0  0  X  X  0  0  X  0
 0  0  0  0  0  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  X  X  0  X  X  0  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+26x^8+16x^9+61x^10+64x^11+40x^12+96x^13+40x^14+64x^15+61x^16+16x^17+26x^18+1x^26

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 1.05e-007 seconds.