The generator matrix

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

generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+204x^119+340x^120+1824x^121+2580x^122+3926x^123+6780x^124+7776x^125+8188x^126+12984x^127+14850x^128+15274x^129+19866x^130+20346x^131+14630x^132+16458x^133+11850x^134+7424x^135+6324x^136+2712x^137+1334x^138+726x^139+324x^140+86x^141+102x^142+84x^143+50x^144+42x^145+18x^146+20x^147+12x^148+6x^149+6x^151

The gray image is a linear code over GF(3) with n=585, k=11 and d=357.
This code was found by Heurico 1.16 in 64.2 seconds.