The generator matrix

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

generates a code of length 26 over Z3[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+52x^51+648x^52+26x^54+2x^78

The gray image is a linear code over GF(3) with n=234, k=6 and d=153.
As d=155 is an upper bound for linear (234,6,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.00538 seconds.