The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  4  2  1  1  2  0  2  2  2  1  1  1
 0  2  0  0  0  2  6 14  8 12 10  8  2 10 14  2 10 14 10 10  2  0  4  4 14  2  6
 0  0  2  0  2  2  2  0  0  4  6  2 14  8  4 14  2  4  8 14  2  2  0 10  6  4  2
 0  0  0  2  2  0  2  2  4  2  6  6 12  6  8 10  4  8  6  6 12 12 14  2 10  8  2
 0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  8  8  8  0  0  8  0  8  8  0  8
 0  0  0  0  0  8  0  0  8  8  8  0  0  8  0  8  0  0  0  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  0  8  8  8  8  8  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+130x^20+358x^21+1025x^22+1924x^23+4024x^24+6704x^25+12153x^26+12724x^27+12343x^28+6772x^29+4079x^30+1900x^31+890x^32+304x^33+147x^34+28x^35+19x^36+6x^37+4x^38+1x^40

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 19.4 seconds.