The generator matrix

 1  0  0  1  1  1  X X^2  1  1  1  1  1
 0  1  0  1  X X^2+X+1  1  0 X^2+X X+1  1  1  X
 0  0  1  1  1  0  1  1 X^2+1 X^2+X+1 X+1 X+1  1
 0  0  0  X  0 X^2+X X^2  X X^2+X  X X^2  0  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+56x^9+154x^10+270x^11+277x^12+512x^13+336x^14+252x^15+113x^16+56x^17+14x^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 1.16 in 0.0171 seconds.