The generator matrix

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

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+66x^4+274x^5+649x^6+2024x^7+2149x^8+2044x^9+658x^10+264x^11+56x^12+2x^13+5x^14

The gray image is a linear code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0339 seconds.