The generator matrix

 1  1  1  1  1  1  1  1  1  1  3  3  3  1
 0  9  0  9  0  9 18 18 18  0  0  9  9  9
 0  0  9 18 18  9  0  9 18  0  9 18  9  0

generates a code of length 14 over Z27 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+18x^25+14x^27+180x^28+6x^30+18x^31+6x^33

The gray image is a code over GF(3) with n=126, k=5 and d=75.
This code was found by Heurico 1.16 in 0.000525 seconds.