The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1 2X  1  1  X  1  1 2X^2+X  X 2X 2X  1  1  1  1  1 2X^2+2X  1  1 X^2  1  1  1
 0  1  1  2 2X^2+X 2X^2+X+2 2X^2+2X+1  1  2 2X  1 X+1 2X+2  1 2X^2+X+2 2X+2  1  1  1  1 2X^2+2  2  0 2X^2+2X 2X  1 2X^2+1 2X+2  X 2X^2+X X+2 X^2
 0  0 2X  0 2X^2 2X^2 2X^2+2X 2X^2+X 2X  0 2X^2 2X 2X^2  X 2X^2+2X 2X^2+2X 2X^2+2X 2X^2+X 2X^2 2X 2X^2+X  X X^2+2X X^2+X X^2+2X 2X^2+X X^2 2X^2 2X^2+2X 2X  X X^2+X
 0  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0  0 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0  0 2X^2  0  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+128x^57+264x^58+582x^59+1236x^60+1524x^61+1884x^62+2488x^63+2598x^64+3024x^65+2650x^66+1842x^67+732x^68+426x^69+60x^70+78x^71+116x^72+30x^73+18x^74+2x^81

The gray image is a linear code over GF(3) with n=288, k=9 and d=171.
This code was found by Heurico 1.16 in 0.499 seconds.