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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+96x^67+144x^68+10x^69+78x^70+288x^71+8x^72+96x^73+6x^75+2x^87

The gray image is a linear code over GF(3) with n=315, k=6 and d=201.
This code was found by Heurico 1.16 in 0.0197 seconds.