The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+65x^20+84x^21+227x^22+558x^23+1437x^24+3670x^25+6935x^26+12030x^27+15422x^28+12126x^29+6979x^30+3706x^31+1441x^32+498x^33+174x^34+90x^35+65x^36+6x^37+17x^38+1x^40+3x^42+1x^46

The gray image is a code over GF(2) with n=224, k=16 and d=80.
This code was found by Heurico 1.16 in 14.4 seconds.