The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+384x^131+882x^132+384x^133+996x^134+820x^135+294x^136+492x^137+770x^138+222x^139+564x^140+498x^141+60x^142+144x^143+2x^144+6x^145+6x^146+8x^147+6x^148+6x^152+12x^156+2x^162+2x^165

The gray image is a linear code over GF(3) with n=612, k=8 and d=393.
This code was found by Heurico 1.16 in 2.02 seconds.