The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X
 0  X  0  0  0  0  0  0  0  0  X  X  X
 0  0  X  0  0  0  0  0  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  X  0  X  X
 0  0  0  0  X  0  0  0  X  0  0  X  X
 0  0  0  0  0  X  0  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  X  X  X  0  0  X

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+55x^8+224x^12+128x^14+87x^16+16x^20+1x^24

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 6.87e-008 seconds.