The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1 X^2+X X^2+X+1 X^2  X
 0  0  1  1 X+1  X  X X^2+X
 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+26x^5+137x^6+168x^7+365x^8+164x^9+134x^10+24x^11+2x^12+2x^13+1x^14

The gray image is a linear code over GF(2) with n=32, k=10 and d=10.
This code was found by Heurico 1.16 in 0.00161 seconds.