The generator matrix

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

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+40x^9+96x^10+324x^11+294x^12+560x^13+280x^14+312x^15+87x^16+40x^17+8x^18+4x^19+2x^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 1.16 in 0.0157 seconds.