The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  1  1  1  8  1 10 14  4  1  2  4  1
 0  1 11  6  1  1  0  3  1  5  1 14  5  1  8  9 14  6  1  5  1  1  1 13 14  4 11
 0  0 12  0  0  0 12  0  4 12 12  0  8  4  0  4  4  8 12  4 12 12  8  8  0  4 12
 0  0  0 12  0  0  0  0  0  0  0  8  0  8  8  8 12 12  4  4  4 12 12  4 12  4 12
 0  0  0  0  4  4  0  8 12  4  0 12  8 12  4 12  4 12 12  0  0  4  0  8  8 12 12
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  0  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  8  8  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+183x^20+84x^21+900x^22+888x^23+3988x^24+7356x^25+12316x^26+14032x^27+12356x^28+7436x^29+4028x^30+824x^31+859x^32+100x^33+164x^34+20x^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 14.8 seconds.