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  3  3  3  0  3  3  3
 0  3 24  0 21 24  9 21  6  9 12  6  9  0 12  3 24  6 18 18 21 12 15 15 18  3 15 21 24 21  3 24  6 12
 0  0  9  9 18 18 18  9  0  9  0  9  0 18  9 18  0 18  0  9  0 18  9 18 18  9  0 18  0  9  0  9 18  0

generates a code of length 34 over Z27 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+108x^65+84x^66+270x^68+144x^69+108x^71+6x^72+6x^75+2x^81

The gray image is a code over GF(3) with n=306, k=6 and d=195.
This code was found by Heurico 1.16 in 0.0124 seconds.