The generator matrix

 1  0  1  1  1 X^2  1  1  1 X^2+X  1  1  1
 0  1  1  0 X^2+X+1  1 X+1  X  0  1  X X+1 X^2+X+1
 0  0  X  0 X^2+X X^2  X X^2 X^2+X X^2+X  X X^2  0
 0  0  0  X  0 X^2+X  X X^2+X  X X^2+X  0 X^2  X
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 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+48x^9+114x^10+228x^11+409x^12+464x^13+385x^14+248x^15+101x^16+32x^17+12x^18+4x^19+1x^20+1x^22

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 0.0237 seconds.