The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+26x^6+83x^8+284x^10+620x^12+640x^14+299x^16+68x^18+20x^20+6x^22+1x^24

The gray image is a linear code over GF(2) with n=26, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0193 seconds.