The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+456x^119+522x^120+828x^121+660x^122+802x^123+576x^124+558x^125+520x^126+582x^127+402x^128+310x^129+114x^130+174x^131+12x^132+6x^133+6x^134+4x^135+12x^137+8x^138+6x^144+2x^150

The gray image is a linear code over GF(3) with n=558, k=8 and d=357.
This code was found by Heurico 1.16 in 0.185 seconds.