The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+906x^122+1638x^123+2034x^124+4626x^125+6286x^126+6552x^127+11400x^128+12062x^129+12888x^130+19170x^131+18486x^132+15372x^133+19110x^134+15618x^135+10026x^136+9636x^137+5510x^138+2556x^139+1776x^140+774x^141+144x^142+252x^143+58x^144+150x^146+50x^147+36x^149+18x^150+6x^152+6x^153

The gray image is a linear code over GF(3) with n=594, k=11 and d=366.
This code was found by Heurico 1.16 in 469 seconds.