The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+510x^107+828x^108+504x^109+1686x^110+1664x^111+936x^112+2568x^113+2824x^114+648x^115+2760x^116+2226x^117+684x^118+978x^119+398x^120+144x^121+138x^122+14x^123+60x^125+48x^126+36x^128+6x^129+12x^131+6x^132+2x^138+2x^144

The gray image is a linear code over GF(3) with n=513, k=9 and d=321.
This code was found by Heurico 1.16 in 3.83 seconds.