The generator matrix

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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+60x^68+2x^69+12x^71+4x^72+2x^75

The gray image is a linear code over GF(3) with n=306, k=4 and d=204.
This code was found by Heurico 1.16 in 0.00759 seconds.