The generator matrix
1 0 0 0 1 1 1 X^2+X 1
0 1 0 0 1 X X^2 0 0
0 0 1 0 1 0 X+1 1 0
0 0 0 1 1 X+1 0 1 0
0 0 0 0 X X X^2+X X^2+X X^2
0 0 0 0 0 X^2 X^2 0 X^2
generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+77x^4+248x^5+1295x^6+2848x^7+7843x^8+8144x^9+7843x^10+2848x^11+1295x^12+248x^13+77x^14+1x^18
The gray image is a linear code over GF(2) with n=36, k=15 and d=8.
This code was found by Heurico 1.16 in 0.509 seconds.