The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1  X X+1  0  X
 0  0  1  1 X+1  X  X X+1
 0  0  0 X^2  0  0 X^2 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+32x^5+116x^6+194x^7+345x^8+190x^9+108x^10+30x^11+6x^12+2x^13

The gray image is a linear code over GF(2) with n=32, k=10 and d=10.
This code was found by Heurico 1.11 in -1.01e-007 seconds.