The generator matrix
1 0 0 0 0 1 1 1
0 1 0 0 0 X 1 X^2+X
0 0 1 0 0 1 X+1 X+1
0 0 0 1 0 1 X 1
0 0 0 0 1 1 0 X
0 0 0 0 0 X^2 X^2 0
generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+48x^3+379x^4+1968x^5+6534x^6+14368x^7+18935x^8+14368x^9+6548x^10+1968x^11+365x^12+48x^13+6x^14
The gray image is a linear code over GF(2) with n=32, k=16 and d=6.
This code was found by Heurico 1.13 in 0.047 seconds.