The generator matrix

 1  0  1  1  1  4  1  1  6  1  1 10  1  1  2  2 14  1  1  2  8  1  1  1  1  6  2  1
 0  1  1  0 11  1 10  5  1  7  6  1  8  3  4  1  1  4  2  1  2 13  9  7 10  1 12  5
 0  0  2  6  4  6 14  4  0  6  4  6  4  0  6  2  0  8  6 12  2 10  2  8  8  2  2  4
 0  0  0 12  0  4  0 12  0  4  4  8  8  0 12  0  4  4 12  8  8  0  4  4  8  4 12  4
 0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  8  8  8  8  8  8  8  8  0  8  0
 0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  0  8  0  0  8  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  0

generates a code of length 28 over Z16 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+60x^21+313x^22+472x^23+1562x^24+3694x^25+7284x^26+12624x^27+13428x^28+12782x^29+7283x^30+3624x^31+1603x^32+474x^33+220x^34+48x^35+44x^36+14x^37+3x^38+2x^40+1x^46

The gray image is a code over GF(2) with n=224, k=16 and d=84.
This code was found by Heurico 1.16 in 14.5 seconds.