The generator matrix

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

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+38x^6+106x^7+183x^8+358x^9+616x^10+938x^11+1200x^12+1302x^13+1220x^14+910x^15+631x^16+386x^17+168x^18+94x^19+32x^20+2x^21+6x^22+1x^24

The gray image is a linear code over GF(2) with n=26, k=13 and d=6.
This code was found by Heurico 1.16 in 0.244 seconds.