The generator matrix

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

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+127x^8+64x^9+616x^10+640x^11+1832x^12+1664x^13+1776x^14+640x^15+655x^16+64x^17+104x^18+8x^20+1x^24

The gray image is a linear code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.16 in 0.289 seconds.