The generator matrix

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

generates a code of length 3 over Z3[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+72x^4+510x^6+144x^7+2x^9

The gray image is a linear code over GF(3) with n=27, k=6 and d=12.
This code was found by Heurico 1.16 in 4.41e-005 seconds.