The generator matrix

 1  0  1  1  1  0  1  1  1  1  X  1  1
 0  1  1  0  1  1  0  X  0  0  0  X  0
 0  0  X  0  0  0  X  X  0  0  X  X  0
 0  0  0  X  0  0  X  0  X  X  0  X  0
 0  0  0  0  X  0  X  X  X  X  X  X  0
 0  0  0  0  0  X  X  X  0  X  0  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+14x^8+38x^10+94x^12+44x^14+45x^16+14x^18+6x^20

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 6.29e-008 seconds.