The generator matrix

 1  0  1  1  1  0  1  1  1  1  0  1  1
 0  1  1  0  1  1  0  X X+1  0  1 X+1 X+1
 0  0  X  0  0  X  X  X  0  0  0  X  0
 0  0  0  X  0  X  X  0  X  0  X  0  0
 0  0  0  0  X  X  X  X  X  X  0  0  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+24x^10+41x^12+37x^14+21x^16+2x^18+1x^20+1x^22

The gray image is a linear code over GF(2) with n=26, k=7 and d=10.
This code was found by Heurico 1.16 in 0.00102 seconds.