The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+36x^9+135x^10+230x^11+385x^12+496x^13+366x^14+228x^15+125x^16+28x^17+11x^18+6x^19+1x^20

The gray image is a linear code over GF(2) with n=52, k=11 and d=18.
This code was found by Heurico 1.11 in 0.015 seconds.