The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  0  1
 0  1  7 26 21  4 20 24 19 23  0  4  3 23
 0  0  9  0 18  9 18  9 18  9 18  9  9 18
 0  0  0  9  9 18 18  9 18 18  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+408x^24+1296x^26+1064x^27+2592x^29+1098x^30+96x^33+6x^36

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 1.11 seconds.