The generator matrix

 1  0  0  1  1  1  X  1  1
 0  1  0  1  X X+1  1  1  0
 0  0  1  X  1 X+1 X+1 X^2  0

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+26x^6+70x^7+75x^8+190x^9+54x^10+50x^11+36x^12+10x^13

The gray image is a linear code over GF(2) with n=36, k=9 and d=12.
This code was found by Heurico 1.11 in -3.24e-008 seconds.