The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+276x^128+262x^129+558x^130+1386x^131+1178x^132+1440x^133+2298x^134+1520x^135+1482x^136+2640x^137+1914x^138+1290x^139+1560x^140+572x^141+522x^142+438x^143+86x^144+30x^145+84x^146+18x^147+6x^148+42x^149+14x^150+18x^152+20x^153+18x^154+6x^155+2x^156+2x^162

The gray image is a linear code over GF(3) with n=612, k=9 and d=384.
This code was found by Heurico 1.16 in 1.27 seconds.