The generator matrix

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

generates a code of length 64 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+1142x^117+2508x^118+4686x^119+8170x^120+11394x^121+16428x^122+22738x^123+28464x^124+36636x^125+44086x^126+49332x^127+55062x^128+58434x^129+51846x^130+46020x^131+37116x^132+25452x^133+15384x^134+8696x^135+4218x^136+2106x^137+944x^138+258x^139+48x^140+140x^141+12x^142+36x^143+48x^144+12x^145+12x^146+6x^147+6x^148

The gray image is a linear code over GF(3) with n=576, k=12 and d=351.
This code was found by Heurico 1.16 in 518 seconds.