The generator matrix

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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+144x^118+372x^119+838x^120+1320x^121+2052x^122+2546x^123+2880x^124+4902x^125+3934x^126+5520x^127+7776x^128+5900x^129+5988x^130+6012x^131+3674x^132+2100x^133+1350x^134+672x^135+282x^136+204x^137+70x^138+126x^139+102x^140+90x^141+78x^142+48x^143+4x^144+30x^145+18x^146+8x^147+6x^149+2x^150

The gray image is a linear code over GF(3) with n=576, k=10 and d=354.
This code was found by Heurico 1.16 in 9.26 seconds.