The generator matrix

 1  0  1  1  1  0  X  1  1
 0  1  1  0 X+1  1 X^2  0  0
 0  0  X X^2+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  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+55x^4+192x^6+96x^7+525x^8+320x^9+504x^10+96x^11+213x^12+40x^14+6x^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 0.00283 seconds.