The generator matrix

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

generates a code of length 3 over Z3[X]/(X^3) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+6x^3+54x^4+552x^6+108x^7+8x^9

The gray image is a linear code over GF(3) with n=27, k=6 and d=9.
This code was found by Heurico 1.16 in 6.79e-005 seconds.