The generator matrix

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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+150x^121+288x^122+266x^123+726x^124+1188x^125+812x^126+1374x^127+1992x^128+1344x^129+2100x^130+2748x^131+1594x^132+1818x^133+1758x^134+560x^135+492x^136+168x^137+18x^138+108x^139+96x^140+4x^141+30x^142+24x^143+2x^144+6x^145+4x^147+4x^150+2x^153+4x^159+2x^165

The gray image is a linear code over GF(3) with n=585, k=9 and d=363.
This code was found by Heurico 1.16 in 3.54 seconds.