The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  2  2  2  2  0  2  2  2
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  4  4  4 12 12 12  4 12  8  4
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  8 12  4  4  8  0  0  4  4 12 12
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8 12  8  8  8  8  0  8 12  4  0  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  8  0  0  8  0  8  0  8  0  8  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  0  0  0  0  8  8  0  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+42x^21+107x^22+164x^23+247x^24+306x^25+651x^26+1520x^27+2114x^28+1570x^29+640x^30+308x^31+223x^32+126x^33+68x^34+56x^35+38x^36+4x^37+5x^38+1x^40+1x^42

The gray image is a code over GF(2) with n=224, k=13 and d=84.
This code was found by Heurico 1.16 in 0.609 seconds.