The generator matrix
1 0 0 1 1 1 X^2+X 1 1
0 1 0 1 0 1 1 0 0
0 0 1 1 1 0 1 0 0
0 0 0 X 0 0 X X^2+X X^2+X
0 0 0 0 X 0 X X^2+X X
0 0 0 0 0 X X X^2 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+145x^4+96x^5+1410x^6+2816x^7+7665x^8+8512x^9+7644x^10+2816x^11+1431x^12+96x^13+130x^14+6x^16
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 0.596 seconds.