The generator matrix

 1  0  0  1  1  1  1  1  1  1 2X^2+2X  1 X^2  1  1  1 2X^2+X 2X X^2 2X^2  1  1  1  1  1 X^2+X  1  1 X^2+2X  1  1  0  1  1  1  1  1 2X^2+X  0 X^2+X  1  1  X  1  1 2X  1  1  1  1  1 2X^2+2X 2X^2+2X  1  1  1  X 2X^2  1  1  1 X^2+2X  1 2X^2+2X
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2  2 2X^2+2X+2 2X^2+X+1  1 X^2+2X+1  1 2X^2+X 2X^2+2X+1 2X+1  1 X^2  1  1 X^2+2X+2 2X^2+2X 2X^2+2 X^2+X 2X^2+X+1  1  2 2X  1 2X^2+1 X+1 2X^2+2X 2X^2+2X+2 X^2+2X 2X^2+X+1 2X^2+X 2X^2+X+2  1  1 X^2+X X^2+2X+2 X^2+2X+2  1 X^2+X  1  1 X+1  1 2X 2X^2+1  X  1  1 2X^2+X X^2+X+1 X^2+2X  1  X 2X+1 X^2+X+1 X^2+2X+2  1 X^2+1  1
 0  0  1 2X^2+2X+1 2X^2+2 X^2+2 2X^2+X+2 X^2 X^2+2X+1 2X^2+1 X^2+2X+1  0 2X^2+2 X^2+2X 2X^2+X+1 X+2 X^2+X+1  1 2X^2+2X+2 2X^2+X X^2 X^2+X+2 2X^2+2X+1 X^2+1 2X^2+X X^2+X  2 2X+2 X^2+1 2X^2+X+2 X+1  1 2X^2+2X 2X^2+2X 2X^2 2X+1 2X^2+2X+2 2X^2+X+2 2X^2+2X  1 2X+2  1 X^2+2X+1 2X^2  1 X^2+2 X^2+2X X+1 X^2+X 2X^2+2X+2 X^2+X+1  0 X^2+X+1 2X^2+X+1 X^2+X+1 2X^2+X+1 2X^2+2X+1  1  1 X^2+2X+2 X^2+X  0 X+2 2X+2
 0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 2X^2 X^2  0 2X^2  0  0 X^2  0 X^2 X^2  0 2X^2 2X^2  0 2X^2  0 X^2  0  0  0  0 X^2 X^2 2X^2 X^2  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2 X^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+816x^120+1224x^121+2196x^122+3462x^123+3438x^124+4374x^125+6172x^126+4914x^127+5796x^128+6092x^129+4716x^130+4500x^131+4488x^132+2610x^133+1998x^134+1266x^135+594x^136+90x^137+218x^138+42x^141+40x^144+2x^147

The gray image is a linear code over GF(3) with n=576, k=10 and d=360.
This code was found by Heurico 1.16 in 10.3 seconds.