The generator matrix

 1  0  0  1  1  1  X  1  1 X^2 X^2+X  0  X
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X^2+1  1  1  1  1
 0  0  1  1 X^2+X+1 X^2+X  1  X X+1  1 X+1 X+1  1
 0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 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+75x^8+160x^9+316x^10+1152x^11+1184x^12+2496x^13+1048x^14+1152x^15+395x^16+160x^17+44x^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 0.139 seconds.