The generator matrix

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

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+55x^4+232x^5+850x^6+1792x^7+2287x^8+1872x^9+844x^10+192x^11+57x^12+8x^13+2x^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 0.0487 seconds.