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.