The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  1  1  1  3  3  1  3  1  1  3  9  9  0  1
 0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9  0

generates a code of length 34 over Z27 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+60x^68+2x^69+12x^71+4x^72+2x^75

The gray image is a code over GF(3) with n=306, k=4 and d=204.
This code was found by Heurico 1.16 in 0.00779 seconds.