The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  X X+1 X+1  0  0
 0  0  1  0  0  0  0  0  1  1 X+1 X+1  0
 0  0  0  1  0  0  0  0  1  X  1  X  0
 0  0  0  0  1  0  0  1  0 X+1 X+1  X  0
 0  0  0  0  0  1  0  1  0  1  X X+1  X
 0  0  0  0  0  0  1  1 X+1  1  0  X  0
 0  0  0  0  0  0  0  X  X  0  X  X  0

generates a code of length 13 over Z2[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+44x^5+155x^6+328x^7+723x^8+1450x^9+2508x^10+3838x^11+4820x^12+5106x^13+4770x^14+3726x^15+2523x^16+1550x^17+748x^18+298x^19+124x^20+42x^21+11x^22+2x^23+1x^24

The gray image is a linear code over GF(2) with n=26, k=15 and d=5.
This code was found by Heurico 1.16 in 3.18 seconds.