The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+66x^64+2x^66+6x^67+2x^69+4x^72

The gray image is a linear code over GF(3) with n=288, k=4 and d=192.
This code was found by Heurico 1.16 in 0.00606 seconds.