The generator matrix

 1  0  0  1  1  1  X X^2  1  0  1  1 X^2+X
 0  1  0  1  X X^2+X+1  1  0 X^2+X  1  X  X  X
 0  0  1  1  1  0  1  1  1  1 X^2+X+1  0  1
 0  0  0  X  0 X^2+X X^2  X  X X^2+X  X X^2+X X^2+X
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 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+108x^9+215x^10+532x^11+676x^12+1016x^13+707x^14+552x^15+171x^16+92x^17+21x^18+4x^19+1x^22

The gray image is a linear code over GF(2) with n=52, k=12 and d=18.
This code was found by Heurico 1.16 in 5.78 seconds.