The generator matrix

 1  0  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1  1  X  1 2X^2 2X^2+2X  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+X 2X^2+2X  1  1  0  1 2X^2  1  1 2X^2+2X  0  1  1 2X^2+2X  1  1 2X 2X^2+X 2X^2+X X^2+X  1  1  1  1  1  1  1 X^2+2X  1 2X  1
 0  1  1  2 2X^2+X 2X^2+X+2  1 2X 2X+2  1 2X^2+2X+1 X+1  0  1 2X 2X+1  1 X+2  1  1 2X^2+X+1  1 2X^2+2 2X^2+X X+2 2X^2+2X+2  0 2X^2+2X+1 2X^2+X X^2+X+2 2X^2 2X+2 2X^2+2X  1  1  2 X^2+X  1 2X^2+2X+1  1 2X^2+2 X^2+2X  1  1 2X+2 X^2  1 2X^2 X^2+2X  1  1  1  1 2X^2+X  X  2 2X  2 2X^2+X+2 2X^2+X+2  1 2X^2+1  1 X+1
 0  0 2X  0 2X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2+2X 2X X^2+2X 2X X^2+2X  X 2X^2+X 2X^2+X 2X^2+X X^2+X  X X^2+X 2X^2+X 2X^2+2X X^2+X 2X^2+X X^2 2X^2 X^2 X^2 2X 2X^2+2X 2X X^2+2X  X 2X^2+2X X^2+X X^2 X^2 X^2+2X  X 2X^2+X 2X X^2 X^2 X^2+2X 2X X^2+X X^2+X  0 2X^2+X  0 X^2+X 2X  0 X^2+2X X^2+2X 2X^2 2X^2 X^2+X 2X^2 2X^2 2X^2+2X 2X
 0  0  0 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2 2X^2 X^2 X^2  0  0 X^2 2X^2 X^2  0 X^2 2X^2 X^2  0 X^2  0  0 2X^2  0 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2  0  0 2X^2 X^2 X^2 2X^2 X^2  0 X^2 X^2  0  0 2X^2 2X^2  0 X^2  0 2X^2 2X^2  0 X^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+72x^120+192x^121+1308x^122+706x^123+900x^124+2334x^125+1238x^126+1404x^127+3432x^128+1526x^129+1188x^130+2586x^131+912x^132+588x^133+876x^134+102x^135+60x^136+78x^137+26x^138+24x^139+42x^140+14x^141+6x^142+12x^143+10x^144+12x^145+18x^146+8x^147+6x^149+2x^162

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 1.17 seconds.