The generator matrix

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

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+216x^15+294x^18+216x^21+2x^27

The gray image is a linear code over GF(3) with n=27, k=6 and d=15.
As d=15 is an upper bound for linear (27,6,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0173 seconds.