The generator matrix

 1  0  1  1  1  0  X  X  1
 0  1  1  0 X+1  1  0 X^2  0
 0  0  X  0  X  0  X  X  0
 0  0  0  X  X X^2+X  X  0  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+93x^4+72x^5+543x^6+864x^7+1411x^8+2224x^9+1411x^10+864x^11+543x^12+72x^13+93x^14+1x^18

The gray image is a linear code over GF(2) with n=36, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0467 seconds.