The generator matrix

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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+246x^120+354x^121+906x^122+1506x^123+1854x^124+2496x^125+3624x^126+3726x^127+4530x^128+6406x^129+5706x^130+6930x^131+6184x^132+4728x^133+3732x^134+2926x^135+1338x^136+660x^137+484x^138+114x^139+78x^140+170x^141+102x^142+72x^143+34x^144+30x^145+30x^146+34x^147+18x^148+6x^149+12x^150+12x^151

The gray image is a linear code over GF(3) with n=585, k=10 and d=360.
This code was found by Heurico 1.16 in 9.46 seconds.