The generator matrix

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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+288x^96+252x^97+414x^98+1684x^99+1512x^100+1998x^101+3816x^102+3924x^103+4824x^104+7494x^105+5724x^106+6336x^107+7046x^108+4536x^109+3618x^110+2738x^111+1476x^112+306x^113+534x^114+72x^115+330x^117+104x^120+18x^123+2x^126+2x^129

The gray image is a linear code over GF(3) with n=477, k=10 and d=288.
This code was found by Heurico 1.16 in 7.5 seconds.