The generator matrix

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

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+25x^6+42x^7+85x^8+166x^9+338x^10+490x^11+582x^12+662x^13+564x^14+462x^15+337x^16+194x^17+94x^18+30x^19+18x^20+2x^21+3x^22+1x^24

The gray image is a linear code over GF(2) with n=26, k=12 and d=6.
This code was found by Heurico 1.16 in 0.0492 seconds.