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

generates a code of length 35 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+16x^69+54x^70+8x^72+2x^105

The gray image is a linear code over GF(3) with n=105, k=4 and d=69.
This code was found by Heurico 1.16 in 0.00449 seconds.