The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+100x^6+384x^7+832x^8+1776x^9+1968x^10+1840x^11+844x^12+336x^13+92x^14+16x^15+3x^16

The gray image is a linear code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.11 in 0.031 seconds.