The generator matrix

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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+756x^122+1338x^123+1710x^124+2184x^125+1882x^126+1512x^127+1974x^128+1700x^129+1296x^130+1518x^131+1272x^132+720x^133+894x^134+508x^135+270x^136+114x^137+16x^138+12x^140+6x^141

The gray image is a linear code over GF(3) with n=576, k=9 and d=366.
This code was found by Heurico 1.16 in 0.91 seconds.