The generator matrix

 1  0  0  1  1  1  1  1 24  1  1  1  1  1  1
 0  1  0  7 15 26 19  2  1 16 26 22 14 22  0
 0  0  1 14 16 26 22  3 26 15 24 21 16 20  0
 0  0  0  9  0  9 18 18  0 18  0  9 18  0  9

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

Homogenous weight enumerator: w(x)=1x^0+502x^24+318x^25+1710x^26+2898x^27+6378x^28+6372x^29+17764x^30+12222x^31+6426x^32+3818x^33+510x^34+72x^35+44x^36+12x^37+2x^39

The gray image is a code over GF(3) with n=135, k=10 and d=72.
This code was found by Heurico 1.16 in 1.16 seconds.