The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  X X^2  X  0  X  0
 0  0  X  0  0  0  0  X  X X^2+X X^2  0  0
 0  0  0  X  0  0  0  X X^2+X X^2 X^2+X  0  0
 0  0  0  0  X  0  X  X X^2 X^2  X  0  0
 0  0  0  0  0  X  X X^2  X X^2 X^2  X  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+84x^6+68x^7+326x^8+328x^9+673x^10+892x^11+964x^12+9712x^13+964x^14+892x^15+673x^16+328x^17+326x^18+68x^19+84x^20+1x^26

The gray image is a linear code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 0.541 seconds.