The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+662x^108+1074x^109+1710x^110+1992x^111+2130x^112+1728x^113+2188x^114+1632x^115+1458x^116+1448x^117+1212x^118+1050x^119+864x^120+414x^121+42x^122+38x^123+6x^124+6x^125+16x^126+6x^127+6x^133

The gray image is a linear code over GF(3) with n=513, k=9 and d=324.
This code was found by Heurico 1.16 in 0.722 seconds.