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

generates a code of length 35 over Z3[X]/(X^3) who�s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+310x^66+324x^68+394x^69+648x^71+384x^72+62x^75+38x^78+18x^81+6x^84+2x^90

The gray image is a linear code over GF(3) with n=315, k=7 and d=198.
This code was found by Heurico 1.16 in 49 seconds.