The generator matrix
1 0 0 0 0 1 1 1
0 1 0 0 0 1 0 0
0 0 1 0 0 1 0 0
0 0 0 1 0 1 0 0
0 0 0 0 1 1 0 0
0 0 0 0 0 X X^2 0
generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+125x^2+492x^3+2230x^4+4540x^5+10931x^6+26712x^7+41010x^8+26712x^9+10931x^10+4540x^11+2230x^12+492x^13+125x^14+1x^16
The gray image is a linear code over GF(2) with n=32, k=17 and d=4.
This code was found by Heurico 1.13 in 0.032 seconds.