The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  1  1  1  4  1  1  1  2  1 14  1  8  0  2  2  1
 0  1 11 14  5  1  0  3  1  6  1 13 15  4  2  1 12  1 10  1  6  1 10  2  1 14  0  0
 0  0 12  4  0  4 12  0  8  8 12  4  0  4  4  4  0 12  0  4  0 12  8  4  8  4  0  0
 0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  0  8  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  0  8  8  8  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8
 0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+43x^20+44x^21+119x^22+236x^23+563x^24+2152x^25+2950x^26+7772x^27+4934x^28+7824x^29+2964x^30+2212x^31+559x^32+216x^33+106x^34+20x^35+37x^36+4x^37+5x^38+5x^40+2x^44

The gray image is a code over GF(2) with n=224, k=15 and d=80.
This code was found by Heurico 1.16 in 3.63 seconds.