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  0  1  1  1  1  1  X  1  1  1  1  X  X  1  1 X^2  X  1  1  1  1  X  1  1  0  X  1
 0  X  0  0  0 2X 2X^2+X 2X^2+2X  X 2X^2+2X 2X^2 2X^2 2X^2+X 2X^2+2X 2X 2X^2+X 2X^2+X 2X^2+X 2X^2+2X X^2+X  0 X^2+X 2X 2X^2+2X 2X^2+2X 2X^2 2X^2 2X  X 2X X^2+X 2X^2+2X X^2+2X X^2  0  X 2X^2+X 2X^2+X 2X^2  0  X 2X^2+2X 2X X^2+X 2X^2+X 2X^2+2X 2X 2X^2 X^2+2X 2X 2X^2+2X 2X^2  X  X 2X^2 X^2+X X^2  X 2X^2+X  X 2X^2 2X^2  X  X X^2+2X
 0  0  X  0 X^2 2X^2 X^2 2X^2  0  0 2X^2+X X^2+2X X^2+2X 2X^2+2X X^2+X  X 2X  X X^2+2X  X X^2+2X X^2+2X 2X^2+X 2X^2+X 2X^2+2X X^2+X 2X^2+2X 2X^2 X^2+2X 2X^2+X X^2+X 2X^2+2X X^2+X X^2+2X 2X 2X^2+X X^2 2X^2+2X 2X^2 2X^2+X X^2  0 2X^2+X X^2+2X 2X^2 2X  0 2X^2+2X 2X X^2+2X 2X^2+X 2X 2X^2 2X 2X X^2 2X^2 X^2+X 2X X^2+2X X^2+2X  X 2X^2+2X X^2+X 2X^2+X
 0  0  0  X 2X^2+2X  0 2X X^2+X  X 2X 2X^2+2X X^2 2X^2  0 X^2 X^2+X X^2+X 2X^2 X^2+2X 2X 2X X^2+2X 2X X^2+X  X 2X^2+X X^2+X  X X^2+2X 2X^2+2X 2X^2 2X^2+X 2X^2  0  X X^2+X X^2 2X  X 2X^2+X X^2+2X X^2+X 2X^2+X  0 X^2 2X^2+2X 2X^2+X 2X^2  0 X^2 X^2  X 2X 2X^2+X 2X^2+2X  X X^2+2X  0 X^2  X 2X^2 X^2 2X^2+2X 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+194x^120+162x^121+396x^122+540x^123+438x^124+696x^125+968x^126+1074x^127+2190x^128+2306x^129+1590x^130+3066x^131+2022x^132+1116x^133+1032x^134+506x^135+252x^136+192x^137+200x^138+144x^139+108x^140+212x^141+48x^142+66x^143+68x^144+24x^145+12x^146+24x^147+12x^148+12x^149+2x^150+6x^152+2x^153+2x^168

The gray image is a linear code over GF(3) with n=585, k=9 and d=360.
This code was found by Heurico 1.16 in 3.39 seconds.