The generator matrix

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

generates a code of length 14 over Z27 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+14x^27+54x^28+6x^30+6x^33

The gray image is a code over GF(3) with n=126, k=4 and d=81.
This code was found by Heurico 1.16 in 0.000449 seconds.