The generator matrix

 1  0  1  1  1 X^2  1  1
 0  1  1  0  1  1 X^2 X^2
 0  0  X  0  0  X X^2  0
 0  0  0  X  0  X X^2 X^2
 0  0  0  0  X  X  X  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+73x^4+32x^5+460x^6+736x^7+1491x^8+736x^9+464x^10+32x^11+67x^12+4x^14

The gray image is a linear code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0104 seconds.