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  0  1  1 X^2+2X  1
 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 2X^2+X X^2+2  1 2X^2+X
 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 X^2+2X+1 2X^2+2X+1  2 2X X^2+2X X^2+X+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 2X^2  0 2X^2 2X^2 X^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+748x^120+1386x^121+1818x^122+3474x^123+4194x^124+3924x^125+5646x^126+6282x^127+4698x^128+5684x^129+6282x^130+3798x^131+3706x^132+3204x^133+1638x^134+1662x^135+522x^136+162x^137+120x^138+56x^141+44x^144

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 8 seconds.