The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  0  1 2X^2+X  1  1  1  1  1  1 2X  1  1  1  1 2X^2+X X^2+X  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1 2X^2+X  1 2X^2+2X+1  1  0  2 2X 2X^2+X+2 2X^2+1 2X+2  1  0 X^2 X^2+X+1 X+1  1  1  2 X^2+2
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2 X^2 2X^2  0 X^2 2X^2 X^2  0 2X^2 2X^2  0  0 X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2 X^2 2X^2  0 X^2 2X^2 X^2  0 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2  0 X^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+288x^59+682x^60+432x^62+1894x^63+864x^65+1908x^66+360x^68+72x^69+58x^72+2x^87

The gray image is a linear code over GF(3) with n=288, k=8 and d=177.
This code was found by Heurico 1.16 in 0.203 seconds.