The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+34x^19+140x^20+218x^21+354x^22+510x^23+880x^24+1204x^25+4692x^26+2120x^27+12368x^28+2088x^29+4836x^30+1280x^31+859x^32+556x^33+312x^34+134x^35+84x^36+30x^37+42x^38+18x^39+4x^40+4x^42

The gray image is a code over GF(2) with n=224, k=15 and d=76.
This code was found by Heurico 1.16 in 14.9 seconds.