The generator matrix

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

generates a code of length 25 over Z3[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+36x^49+20x^51+18x^52+4x^54+2x^57

The gray image is a linear code over GF(3) with n=225, k=4 and d=147.
This code was found by Heurico 1.16 in 0.0025 seconds.