The generator matrix

 1  0  0  1  1  1  0  1  1  X  1  1  1
 0  1  0  1  X X+1  1  0  X  0  1  1 X+1
 0  0  1  1  1  0 X+1  X X+1  1 X+1 X+1 X+1
 0  0  0  X  0  X  X  X  X  X  0  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+11x^10+24x^11+24x^12+26x^13+14x^14+6x^15+7x^16+6x^17+7x^18+2x^19

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 0.000582 seconds.