The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^21+152x^22+252x^23+526x^24+1184x^25+1933x^26+2622x^27+2980x^28+2656x^29+1940x^30+1170x^31+503x^32+216x^33+130x^34+50x^35+20x^36+6x^37+4x^38+2x^39+2x^40+1x^42

The gray image is a code over GF(2) with n=224, k=14 and d=84.
This code was found by Heurico 1.16 in 6.9 seconds.