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

generates a code of length 69 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+228x^138+4x^144+6x^147+4x^153

The gray image is a code over GF(3) with n=621, k=5 and d=414.
This code was found by Heurico 1.16 in 0.109 seconds.