The generator matrix

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

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+24x^5+60x^6+104x^7+141x^8+104x^9+44x^10+24x^11+10x^12

The gray image is a linear code over GF(2) with n=32, k=9 and d=10.
This code was found by Heurico 1.16 in 0.00337 seconds.