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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+48x^67+16x^69+8x^72+6x^76+2x^78

The gray image is a linear code over GF(3) with n=102, k=4 and d=67.
This code was found by Heurico 1.16 in 0.00475 seconds.