The generator matrix

 1  0  1  1  1  1  1 21  1  1  1  1  1  1  1  1
 0  1  7 26  4 21 20  1 24 19 23 20 21 16  0 16
 0  0  9  0 18 18  9  9  0 18  0 18  9  0 18  9

generates a code of length 16 over Z27 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+84x^28+36x^29+418x^30+282x^31+252x^32+778x^33+264x^34+36x^35+14x^36+18x^37+2x^39+2x^42

The gray image is a code over GF(3) with n=144, k=7 and d=84.
This code was found by Heurico 1.16 in 0.00364 seconds.