The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X  0  0  0  X X^2+X  X  0
 0  0  X  0  X  X X^2+X  0  0
 0  0  0  X  X  0 X^2+X  X  0
 0  0  0  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0
 0  0  0  0  0  0 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+77x^4+56x^5+175x^6+224x^7+259x^8+2512x^9+259x^10+224x^11+175x^12+56x^13+77x^14+1x^18

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 0.0133 seconds.