The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1  1
 0  1 16 26 21  4 20  1 24 19 23  1  9 12  7  6

generates a code of length 16 over Z27 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+152x^30+144x^31+54x^32+300x^33+72x^34+2x^36+4x^39

The gray image is a code over GF(3) with n=144, k=6 and d=90.
This code was found by Heurico 1.16 in 0.000842 seconds.