The generator matrix

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

generates a code of length 3 over Z3[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+36x^2+6x^3+486x^4+144x^5+4764x^6+972x^7+144x^8+8x^9

The gray image is a linear code over GF(3) with n=27, k=8 and d=6.
This code was found by Heurico 1.16 in 0.00062 seconds.