The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  1
 0  X  0  0  0  0  0  0  X  0  X  X  0
 0  0  X  0  0  0  0  0  X  X  X  0  0
 0  0  0  X  0  0  0  X  0  X  0  X  0
 0  0  0  0  X  0  0  X  0  0  X  X  0
 0  0  0  0  0  X  0  X  X  0  0  X  0
 0  0  0  0  0  0  X  X  X  X  X  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+26x^8+12x^10+32x^11+24x^12+64x^13+28x^14+32x^15+13x^16+20x^18+4x^22

The gray image is a linear code over GF(2) with n=26, k=8 and d=8.
This code was found by Heurico 1.16 in -3.81e-008 seconds.