The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1  1  6  2  1  1  0  4  1  1  4  1  1  1  1
 0  1 11  6  5  1  0  3  1 13  1  6  3  8  1  1  9  4  1  1 13  7  0 12 14  0  6
 0  0 12  0  0  4  4  4  0  0 12  0  8  8  0 12  8 12 12  8  4 12  4  8  8  4  8
 0  0  0 12  0  4  4  4  4  4  8  8  0  4  0  8  0  0  4 12  8  0  4  8 12  4  0
 0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  0  0  0  8  8  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  8  8  0  8  8
 0  0  0  0  0  0  0  8  8  0  0  8  8  8  8  0  8  0  8  8  8  0  8  0  8  8  8

generates a code of length 27 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+198x^20+24x^21+894x^22+208x^23+6550x^24+1512x^25+20990x^26+4704x^27+21092x^28+1512x^29+6538x^30+208x^31+921x^32+24x^33+122x^34+37x^36+1x^52

The gray image is a code over GF(2) with n=216, k=16 and d=80.
This code was found by Heurico 1.16 in 18.4 seconds.