The generator matrix

 1  1  1  1  1  1  X  X  1
 0  X  0  0  0  X X^2 X^2  0
 0  0  X  0  X  X  X X^2  0
 0  0  0  X  X  0  0 X^2  0
 0  0  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2 X^2  0  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+42x^4+36x^5+90x^6+112x^7+374x^8+728x^9+388x^10+112x^11+90x^12+36x^13+34x^14+5x^16

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 0.00385 seconds.