The generator matrix

 1  1  1  1  X  X  X  X  1
 0  X  0  X  0  X  X  0  0
 0  0  X  X  X  X  0  0  0
 0  0  0 X^2  0  0  0 X^2  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+45x^4+32x^5+79x^6+320x^7+131x^8+832x^9+131x^10+320x^11+79x^12+32x^13+45x^14+1x^18

The gray image is a linear code over GF(2) with n=36, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00366 seconds.