The generator matrix

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

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+108x^117+204x^118+456x^119+804x^120+1488x^121+1452x^122+2518x^123+4026x^124+3372x^125+4374x^126+7602x^127+4920x^128+5884x^129+7662x^130+4380x^131+3534x^132+3384x^133+1206x^134+634x^135+306x^136+180x^137+186x^138+66x^139+54x^140+84x^141+24x^142+12x^143+74x^144+24x^145+6x^146+18x^147+2x^150+2x^153+2x^156

The gray image is a linear code over GF(3) with n=576, k=10 and d=351.
This code was found by Heurico 1.16 in 9.69 seconds.