The generator matrix

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

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+26x^4+108x^5+160x^6+468x^7+522x^8+468x^9+160x^10+108x^11+26x^12+1x^16

The gray image is a linear code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00259 seconds.