The generator matrix

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

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+180x^118+222x^119+316x^120+414x^121+744x^122+826x^123+846x^124+1482x^125+2042x^126+1638x^127+2034x^128+2824x^129+1368x^130+1632x^131+1144x^132+426x^133+324x^134+194x^135+234x^136+186x^137+130x^138+144x^139+126x^140+38x^141+78x^142+30x^143+16x^144+18x^145+24x^146+2x^159

The gray image is a linear code over GF(3) with n=576, k=9 and d=354.
This code was found by Heurico 1.16 in 2.88 seconds.