The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+196x^20+36x^21+604x^22+504x^23+2098x^24+3420x^25+6284x^26+6416x^27+6380x^28+3420x^29+2104x^30+504x^31+573x^32+36x^33+156x^34+30x^36+4x^38+2x^44

The gray image is a code over GF(2) with n=216, k=15 and d=80.
This code was found by Heurico 1.16 in 6.76 seconds.