The generator matrix

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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+510x^120+414x^121+216x^122+1582x^123+1044x^124+216x^125+2674x^126+2484x^127+486x^128+3374x^129+2394x^130+432x^131+2156x^132+954x^133+108x^134+438x^135+110x^138+72x^141+8x^144+6x^150+2x^153+2x^156

The gray image is a linear code over GF(3) with n=576, k=9 and d=360.
This code was found by Heurico 1.16 in 29.2 seconds.