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  1  1  1  1  1  1 18
 0  3  0  0 24 21 15  3 24  9  3 18 24 21 21 15 24  9 21  0  3 24 15 18 15  9  9 21 15  9 15  0  6  3
 0  0  3 24  9  6 21  3  6 18  3 21  0 15 18  3  6 15  6 12  9  0 15 15 21 18 21 18 24  9  6 15  0 21
 0  0  0  9  0  0 18  9 18 18 18 18  9 18 18  0  9 18  9  9  9 18  0  0  9  9  9  9 18  9  0 18 18  0

generates a code of length 34 over Z27 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+252x^62+160x^63+426x^65+666x^66+3216x^68+1188x^69+174x^71+98x^72+168x^74+54x^75+132x^77+18x^78+6x^80+2x^99

The gray image is a code over GF(3) with n=306, k=8 and d=186.
This code was found by Heurico 1.16 in 0.271 seconds.