The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+846x^59+1404x^60+936x^61+3216x^62+2342x^63+1692x^64+3606x^65+2318x^66+936x^67+1692x^68+636x^69+24x^71+12x^72+12x^74+10x^75

The gray image is a linear code over GF(3) with n=288, k=9 and d=177.
This code was found by Heurico 1.16 in 3.41 seconds.