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

generates a code of length 34 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+138x^63+162x^66+1458x^68+324x^69+70x^72+32x^81+2x^99

The gray image is a linear code over GF(3) with n=306, k=7 and d=189.
This code was found by Heurico 1.16 in 1.03 seconds.