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

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+464x^120+36x^122+1086x^123+54x^124+288x^125+2030x^126+324x^127+864x^128+4090x^129+2106x^130+1152x^131+4066x^132+432x^133+576x^134+988x^135+580x^138+336x^141+168x^144+32x^147+6x^153+2x^159+2x^171

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 9.62 seconds.