The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  1  1
 0  X  0  X  0  0  X X^2+X X^2 X^2 X^2 X^2  0
 0  0  X  X  0 X^2+X  X X^2  X  X  X  X  0
 0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  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+24x^9+31x^10+128x^11+59x^12+464x^13+67x^14+128x^15+34x^16+24x^17+29x^18+1x^20+1x^22

The gray image is a linear code over GF(2) with n=52, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00542 seconds.