The generator matrix

 1  0  0  0  1  1  1 24  1  1 18  6 21  1  1  1
 0  1  0  0 15 19 16  1 18  7  1  1  1 10 25 15
 0  0  1  0 16 19 14 25 24  2  6 21 17 23  9 15
 0  0  0  1 14 21 17  2  4  1 20 10 14  9 25 16

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

Homogenous weight enumerator: w(x)=1x^0+342x^24+354x^25+3852x^26+4762x^27+17886x^28+17802x^29+68946x^30+66876x^31+118152x^32+130018x^33+67164x^34+25362x^35+8482x^36+1266x^37+72x^38+72x^39+30x^40+2x^42

The gray image is a code over GF(3) with n=144, k=12 and d=72.
This code was found by Heurico 1.16 in 84.8 seconds.