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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 133.

Homogenous weight enumerator: w(x)=1x^0+36x^133+162x^134+14x^135+18x^136+6x^138+4x^141+2x^168

The gray image is a linear code over GF(3) with n=603, k=5 and d=399.
This code was found by Heurico 1.16 in 0.0973 seconds.