The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 130.

Homogenous weight enumerator: w(x)=1x^0+156x^130+252x^131+714x^132+816x^133+696x^134+596x^135+642x^136+402x^137+630x^138+552x^139+276x^140+356x^141+246x^142+150x^143+36x^144+6x^145+4x^147+2x^150+6x^151+6x^152+6x^153+6x^154+2x^156+2x^159

The gray image is a linear code over GF(3) with n=612, k=8 and d=390.
This code was found by Heurico 1.16 in 0.228 seconds.