The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1 2X^2+X  1  1  1  0  1  1  1  1 2X  1  1  1 X^2+X  1  1 X^2+2X  1  1  1  1  1  1  0  1 X^2  1  1  1  1  0  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2+X X^2 2X  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X^2+1 2X+2  1 2X^2+2X+1 2X^2+X  1  2  0 2X  1 X+1 2X^2+X+2 2X^2+1 2X+2  1 X^2 X^2+2X+1 X^2+2  1 X^2+X X^2+X+1  1 2X^2+X+2 X^2+2X+2 2X 2X^2+1 X^2+2X X^2+X+2  1 X^2+1  1 2X X^2+2X 2X^2+1 2X^2+X+2  1 X^2+1 X^2+X+2  1  0 X^2 2X^2+X 2X^2+2X  0 2X^2 X^2 2X^2+X X^2+X 2X^2+2X+1 X^2+2X+1 X+1  1 X^2+2X  2  1  X  1 2X+2 2X^2+X+1
 0  0 2X^2  0 2X^2 X^2 X^2  0  0 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2 X^2 2X^2 X^2  0 X^2 2X^2  0 X^2 2X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2  0  0 2X^2  0 2X^2  0 2X^2 X^2 X^2 2X^2 2X^2  0 X^2 2X^2 X^2  0 X^2 X^2  0 X^2 2X^2 2X^2 2X^2  0 2X^2  0  0 2X^2 2X^2  0  0 2X^2 X^2 2X^2  0
 0  0  0 X^2 X^2 2X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2 X^2 X^2  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 X^2 X^2 X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0 2X^2 X^2 2X^2 X^2  0  0 2X^2 X^2  0 X^2 2X^2  0 2X^2 2X^2 2X^2  0 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+180x^130+306x^131+1000x^132+324x^133+612x^134+812x^135+432x^136+540x^137+684x^138+396x^139+396x^140+614x^141+114x^142+90x^143+40x^144+2x^150+12x^151+4x^159+2x^171

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 0.292 seconds.