The generator matrix

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

generates a code of length 6 over Z3[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+36x^11+24x^12+18x^14+2x^18

The gray image is a linear code over GF(3) with n=18, k=4 and d=11.
As d=11 is an upper bound for linear (18,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000111 seconds.