The generator matrix

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

generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+36x^11+186x^12+18x^14+2x^18

The gray image is a linear code over GF(3) with n=54, k=5 and d=33.
As d=35 is an upper bound for linear (54,5,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.000114 seconds.