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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+48x^57+112x^60+268x^63+1458x^64+232x^66+24x^69+20x^72+6x^75+8x^78+6x^81+2x^84+2x^90

The gray image is a linear code over GF(3) with n=288, k=7 and d=171.
This code was found by Heurico 1.16 in 0.0256 seconds.