The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+534x^60+936x^61+360x^62+996x^63+1044x^64+576x^65+936x^66+936x^67+36x^68+150x^69+18x^72+36x^75+2x^81

The gray image is a linear code over GF(3) with n=288, k=8 and d=180.
This code was found by Heurico 1.16 in 40.1 seconds.