The generator matrix

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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+246x^122+234x^123+738x^124+546x^125+674x^126+606x^127+702x^128+660x^129+408x^130+546x^131+448x^132+468x^133+216x^134+42x^136+6x^139+12x^143+4x^147+2x^150+2x^165

The gray image is a linear code over GF(3) with n=576, k=8 and d=366.
This code was found by Heurico 1.16 in 9.04 seconds.