The generator matrix
1 0 1 1 1 0 1 1
0 1 X+1 X^2+X 1 1 0 0
0 0 X^2 0 0 X^2 0 0
0 0 0 X^2 0 X^2 0 0
0 0 0 0 X^2 X^2 0 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+18x^4+32x^5+40x^6+96x^7+138x^8+96x^9+40x^10+32x^11+18x^12+1x^16
The gray image is a linear code over GF(2) with n=32, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000377 seconds.