The generator matrix

 1  0  1  1  1  1  1 21  1 18  1  1  1  1
 0  1  1 26 18 17 16  1  2  1 16 20  4 23
 0  0 24  9 21 12 15  9  3 12 18  6  9 24

generates a code of length 14 over Z27 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+328x^24+96x^25+882x^26+978x^27+1440x^28+1692x^29+970x^30+72x^31+18x^32+68x^33+12x^34+2x^36+2x^39

The gray image is a code over GF(3) with n=126, k=8 and d=72.
This code was found by Heurico 1.16 in 2.18 seconds.