The generator matrix

 1  1  1  1  1  1  1  X  1  X  X  1  1
 0  X  0  0  0  0  0  X  X  X  0  0  0
 0  0  X  0  0  0  X  X  X  X  X  0  0
 0  0  0  X  0  0  X  0  0  X  X  0  0
 0  0  0  0  X  0  X  0  X  0  X  0  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+16x^8+8x^10+46x^12+24x^14+23x^16+10x^20

The gray image is a linear code over GF(2) with n=26, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000737 seconds.