The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+80x^5+296x^6+864x^7+1742x^8+2208x^9+1776x^10+864x^11+272x^12+80x^13+8x^14+1x^16

The gray image is a linear code over GF(2) with n=36, k=13 and d=10.
This code was found by Heurico 1.11 in 0.015 seconds.