The generator matrix

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

generates a code of length 32 over Z3[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+440x^57+762x^58+1914x^59+3756x^60+3474x^61+6096x^62+8336x^63+6294x^64+9996x^65+8872x^66+4098x^67+2838x^68+1578x^69+414x^70+42x^71+84x^72+24x^73+12x^74+18x^75

The gray image is a linear code over GF(3) with n=288, k=10 and d=171.
This code was found by Heurico 1.16 in 3.38 seconds.