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  1  1  1  1  1  1  1  1  X  1  X  1  1  1  0  1  1  1  1  0  1  1  1 2X^2  X  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X 2X^2+X 2X^2  0 2X^2+X 2X^2+2X X^2 2X^2+2X 2X^2+2X X^2+X X^2 X^2+X 2X^2+X 2X^2 2X 2X^2+2X 2X 2X^2+X 2X  0 2X^2 2X^2+2X 2X^2+X X^2 2X^2+2X 2X 2X^2 X^2+X 2X X^2+X  X  X X^2+X 2X^2+2X  X  X X^2+X  0 2X  0  0 X^2+2X 2X^2 X^2+2X  X 2X 2X 2X^2 2X^2  0 X^2 X^2  X  X 2X^2+X  0
 0  0  X 2X  0 X^2+2X X^2+X  X X^2+2X 2X^2+2X  X 2X^2 X^2+X X^2+X 2X  0 2X^2+2X X^2  0  X 2X 2X^2+X X^2+2X X^2+X 2X^2  0 X^2+2X 2X 2X^2+X  X 2X^2 2X^2+2X 2X^2 2X^2+2X 2X^2 X^2+X X^2+X 2X^2+X X^2+2X 2X 2X^2  0 X^2+X 2X^2 2X X^2+2X X^2 X^2 2X^2+X X^2+X  X 2X^2+X 2X  0 2X^2  0 X^2+2X  X 2X  0 X^2  X 2X  0
 0  0  0 X^2  0  0 2X^2  0  0 X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2  0  0 X^2  0  0 2X^2 2X^2  0 2X^2  0  0 2X^2  0 2X^2 2X^2 X^2 2X^2  0 X^2  0 2X^2  0 X^2 X^2 X^2 2X^2 X^2 2X^2  0 X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2 2X^2  0  0 X^2
 0  0  0  0 X^2 2X^2  0 X^2 2X^2  0 2X^2 X^2  0  0  0 X^2 2X^2  0 X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2  0  0 2X^2  0 2X^2 X^2 X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 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+110x^117+96x^118+138x^119+570x^120+228x^121+264x^122+724x^123+924x^124+540x^125+2566x^126+2832x^127+990x^128+3948x^129+2778x^130+714x^131+770x^132+180x^133+144x^134+346x^135+126x^136+54x^137+282x^138+72x^139+48x^140+102x^141+30x^142+18x^143+46x^144+24x^145+6x^146+2x^147+6x^150+2x^156+2x^174

The gray image is a linear code over GF(3) with n=576, k=9 and d=351.
This code was found by Heurico 1.16 in 2.03 seconds.