The generator matrix
1 1 1 1 1 1 X 1 1
0 X 0 0 0 0 X X^2 0
0 0 X 0 0 0 X X^2+X X^2
0 0 0 X 0 X 0 X X^2
0 0 0 0 X X 0 X^2 0
0 0 0 0 0 X^2 X^2 X^2 0
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+46x^4+52x^5+142x^6+240x^7+830x^8+1464x^9+844x^10+240x^11+142x^12+52x^13+38x^14+5x^16
The gray image is a linear code over GF(2) with n=36, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0135 seconds.