The generator matrix

 1  0  1  1  1  1  1 21  1  1  1  1  1  1  1  1
 0  1  7 26 21  4 20  1 19 16 19  0  4 26  0  0
 0  0  9  0  0  0 18  9 18 18 18  0 18  0 18  0
 0  0  0  9  0  9  9  9 18  9  0  0 18  0  9  9
 0  0  0  0 18 18  0 18 18  9 18  9  9 18  9  9

generates a code of length 16 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+42x^24+18x^25+84x^26+192x^27+792x^28+186x^29+2428x^30+2970x^31+4770x^32+4498x^33+2952x^34+258x^35+320x^36+72x^37+48x^38+38x^39+14x^42

The gray image is a code over GF(3) with n=144, k=9 and d=72.
This code was found by Heurico 1.16 in 0.172 seconds.