The generator matrix

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

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+78x^18+2x^27

The gray image is a linear code over GF(3) with n=27, k=4 and d=18.
As d=18 is an upper bound for linear (27,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000175 seconds.