The generator matrix

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

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+596x^96+630x^97+1638x^98+2558x^99+1734x^100+1908x^101+2638x^102+1440x^103+1878x^104+1696x^105+762x^106+822x^107+984x^108+276x^109+66x^110+18x^111+12x^112+6x^113+6x^114+6x^115+6x^117+2x^120

The gray image is a linear code over GF(3) with n=459, k=9 and d=288.
This code was found by Heurico 1.16 in 0.635 seconds.