The generator matrix

 1  1
 0 2X^2+X

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

Homogenous weight enumerator: w(x)=1x^0+12x^2+4x^3+198x^4+24x^5+4x^6

The gray image is a linear code over GF(3) with n=18, k=5 and d=6.
This code was found by Heurico 1.16 in 1.38e-005 seconds.