The generator matrix

 1  1  1  1  1  1  1  1  1  3  1  3  1  1  1  1
 0  9 18  0  9 18  0  9 18  9  0 18  9 18  0  9

generates a code of length 16 over Z27 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+12x^31+54x^32+4x^33+6x^34+2x^36+2x^42

The gray image is a code over GF(3) with n=144, k=4 and d=93.
This code was found by Heurico 1.16 in 0.000631 seconds.