The generator matrix

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

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+7x^10+8x^12+32x^13+8x^14+7x^16+1x^26

The gray image is a linear code over GF(2) with n=26, k=6 and d=10.
This code was found by Heurico 1.16 in 0.000546 seconds.