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

generates a code of length 26 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+144x^48+72x^49+72x^50+76x^51+1512x^52+72x^53+134x^54+18x^56+36x^58+48x^60+2x^78

The gray image is a linear code over GF(3) with n=234, k=7 and d=144.
This code was found by Heurico 1.16 in 25.4 seconds.