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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+476x^129+564x^130+732x^131+1006x^132+552x^133+474x^134+578x^135+480x^136+432x^137+560x^138+330x^139+132x^140+192x^141+6x^142+12x^143+4x^144+6x^145+8x^147+6x^148+2x^153+6x^156+2x^159

The gray image is a linear code over GF(3) with n=603, k=8 and d=387.
This code was found by Heurico 1.16 in 0.231 seconds.