The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^24+24x^25+60x^26+8x^27+552x^28+24x^29+6x^30+12x^31+24x^32+4x^33+6x^34+2x^42

The gray image is a code over GF(3) with n=126, k=6 and d=72.
This code was found by Heurico 1.16 in 0.0012 seconds.