The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+240x^103+558x^104+920x^105+876x^106+558x^107+790x^108+408x^109+498x^110+706x^111+522x^112+318x^113+76x^114+54x^115+2x^120+6x^121+6x^123+12x^125+10x^126

The gray image is a linear code over GF(3) with n=486, k=8 and d=309.
This code was found by Heurico 1.16 in 0.139 seconds.