The generator matrix
1 1 1 1 1 1 X 1 1
0 X 0 0 0 0 0 X X^2
0 0 X 0 0 0 0 X X^2+X
0 0 0 X 0 0 X X^2 0
0 0 0 0 X 0 X X^2+X X
0 0 0 0 0 X X X 0
0 0 0 0 0 0 X^2 0 X^2
generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+24x^3+114x^4+272x^5+540x^6+1000x^7+3456x^8+5600x^9+3400x^10+1000x^11+582x^12+272x^13+92x^14+24x^15+7x^16
The gray image is a linear code over GF(2) with n=36, k=14 and d=6.
This code was found by Heurico 1.16 in 0.185 seconds.