The generator matrix

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

generates a code of length 15 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+84x^24+60x^25+144x^26+328x^27+612x^28+108x^29+3300x^30+1206x^31+162x^32+334x^33+48x^34+72x^35+82x^36+18x^37+2x^42

The gray image is a code over GF(3) with n=135, k=8 and d=72.
This code was found by Heurico 1.16 in 0.0367 seconds.