The generator matrix

 1  0  1  1  1  1  1  1 2X^2  1  1  0  1  1 2X  1  1  1 2X^2+X  1 2X  1  1  1 2X^2+X  1 X^2+X  1  1  X  1  1
 0  1  1  2 2X^2 2X^2+2  0 2X+1  1 X^2+1  2  1 2X 2X^2+X+2  1 X^2+2X+2 2X^2+X 2X+2  1 X^2+X  1 X^2+X+2 2X^2+2X 2X+2  1 2X  1 X^2+X 2X^2+2X+2  1 2X^2+1 2X
 0  0 2X X^2 X^2+X 2X^2+X X^2+2X  X  X 2X^2+2X X^2+2X X^2+2X 2X^2 X^2  0 2X^2+X  0 2X X^2  X 2X 2X X^2+X 2X^2 2X 2X^2+2X  X X^2+2X  X X^2+X 2X^2 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+198x^59+260x^60+786x^61+762x^62+578x^63+1362x^64+726x^65+658x^66+762x^67+390x^68+10x^69+24x^71+18x^72+6x^74+12x^75+6x^76+2x^84

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 0.061 seconds.