The generator matrix

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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+222x^123+768x^124+906x^125+746x^126+684x^127+612x^128+430x^129+504x^130+594x^131+378x^132+408x^133+156x^134+68x^135+42x^136+6x^141+12x^142+4x^144+12x^145+6x^147+2x^156

The gray image is a linear code over GF(3) with n=576, k=8 and d=369.
This code was found by Heurico 1.16 in 0.212 seconds.