The generator matrix

 1  1
 0 2X+1

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

Homogenous weight enumerator: w(x)=1x^0+12x^2+4x^3+36x^4+24x^5+4x^6

The gray image is a linear code over GF(3) with n=6, k=4 and d=2.
As d=2 is an upper bound for linear (6,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 1.41e-005 seconds.