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

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+696x^59+1572x^60+1314x^61+2382x^62+2716x^63+2256x^64+2886x^65+2436x^66+1272x^67+1314x^68+762x^69+12x^70+6x^71+40x^72+6x^73+6x^74+6x^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 1.57 seconds.