The generator matrix

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

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+24x^67+36x^68+12x^70+4x^75+4x^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 0.00258 seconds.