The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1  9  1  1  1 12  1  1  1  6  1  1  1  1  1  1  1  1 18  3
 0  1 16 26 21  4 20  1 24 19 23  1  9  7  8  1 12 13 11  1  6 10  5  1 18  3 25 22 15  1 17  2  1  1

generates a code of length 34 over Z27 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+96x^67+576x^68+48x^70+4x^75+4x^78

The gray image is a code over GF(3) with n=306, k=6 and d=201.
This code was found by Heurico 1.16 in 0.00597 seconds.