The generator matrix

 1  0  0  0  1  1  1 X^2  1  X  1  1  1
 0  1  0  0 X^2  1 X^2+X+1  1 X^2+X  X  0 X^2+1  0
 0  0  1  0 X^2+1  1  X X^2+1  1  0 X^2+X+1 X^2+X+1 X^2
 0  0  0  1  1 X^2 X+1 X^2+X+1  X  1  X X^2 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+80x^9+267x^10+520x^11+734x^12+850x^13+811x^14+520x^15+223x^16+76x^17+9x^18+2x^20+2x^21+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 0.062 seconds.