The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+33x^8+58x^9+90x^10+186x^11+375x^12+532x^13+422x^14+196x^15+66x^16+50x^17+30x^18+2x^19+5x^20+2x^22

The gray image is a linear code over GF(2) with n=52, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0176 seconds.