The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+348x^129+18x^130+838x^132+108x^133+324x^134+1556x^135+702x^136+648x^137+1314x^138+144x^139+204x^141+170x^144+96x^147+72x^150+8x^153+6x^156+2x^159+2x^189

The gray image is a linear code over GF(3) with n=612, k=8 and d=387.
This code was found by Heurico 1.16 in 0.4 seconds.