The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+278x^27+234x^30+144x^33+72x^36

The gray image is a linear code over GF(3) with n=45, k=6 and d=27.
As d=27 is an upper bound for linear (45,6,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0235 seconds.