The generator matrix

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

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+88x^5+172x^6+488x^7+557x^8+488x^9+156x^10+88x^11+10x^12

The gray image is a linear code over GF(2) with n=32, k=11 and d=10.
This code was found by Heurico 1.11 in 0.016 seconds.