The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+96x^67+576x^68+48x^70+4x^75+4x^78

The gray image is a linear code over GF(3) with n=306, k=6 and d=201.
This code was found by Heurico 1.16 in 0.00599 seconds.