The generator matrix

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

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+92x^9+282x^10+426x^11+860x^12+738x^13+892x^14+468x^15+259x^16+64x^17+10x^18+2x^19+2x^21

The gray image is a linear code over GF(2) with n=52, k=12 and d=18.
This code was found by Heurico 1.11 in 0.015 seconds.