The generator matrix

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

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+816x^118+1434x^119+2280x^120+4332x^121+6426x^122+7320x^123+9894x^124+11952x^125+13874x^126+17394x^127+18198x^128+18674x^129+18474x^130+15876x^131+11432x^132+8454x^133+4734x^134+2436x^135+1596x^136+942x^137+88x^138+168x^139+144x^140+22x^141+84x^142+72x^143+6x^144+12x^145+12x^148

The gray image is a linear code over GF(3) with n=576, k=11 and d=354.
This code was found by Heurico 1.16 in 99.1 seconds.