The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  4  2 12  2  1  8  2  8  4  2  2  1
 0  2  0  0  0  8  8  8  8  2 14 10 14  6 12  4 10 12 10  2  2 14  2 12  8  8  0
 0  0  2  0  0 12  6  2  2  2  4 14  4 10  0  2 14  2  4  6 12 10  8  2  4 14  0
 0  0  0  2  0  6  6  6  4  0 12  2  2 10 12  4 14  6  0  4  2  6  2  8 14  2  0
 0  0  0  0  2  2  4  6  2  8 10 10 14  4 10 12  6 12  4 12  8  8 12  6 12  4  8

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

Homogenous weight enumerator: w(x)=1x^0+79x^20+430x^21+1098x^22+2084x^23+4342x^24+7266x^25+11044x^26+12516x^27+11331x^28+7580x^29+4259x^30+2036x^31+959x^32+314x^33+138x^34+20x^35+24x^36+10x^37+5x^38

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 20.1 seconds.