The generator matrix

 1  0  1
 0  1 2X^2+2X+1
 0  0 2X^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+216x^4+1524x^6+432x^7+8x^9

The gray image is a linear code over GF(3) with n=27, k=7 and d=9.
This code was found by Heurico 1.16 in 0.000172 seconds.