The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  3  0  9 24 21  3 15 24  9  9 15 12 12
 0  0  3 15  9  6  3 21 15  0  6 18 24  6

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

Homogenous weight enumerator: w(x)=1x^0+72x^24+96x^25+90x^26+68x^27+1602x^28+36x^29+48x^30+72x^31+36x^32+52x^33+12x^34+2x^42

The gray image is a code over GF(3) with n=126, k=7 and d=72.
This code was found by Heurico 1.16 in 0.00476 seconds.