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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+124x^54+72x^57+264x^60+784x^63+4374x^64+702x^66+48x^69+114x^72+36x^75+12x^78+28x^81+2x^90

The gray image is a linear code over GF(3) with n=288, k=8 and d=162.
This code was found by Heurico 1.16 in 1.14 seconds.