The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+360x^127+810x^128+732x^129+666x^130+750x^131+508x^132+540x^133+450x^134+498x^135+468x^136+522x^137+116x^138+48x^139+60x^140+2x^141+12x^145+2x^147+6x^148+2x^153+6x^154+2x^156

The gray image is a linear code over GF(3) with n=594, k=8 and d=381.
This code was found by Heurico 1.16 in 0.211 seconds.