The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+102x^20+20x^21+294x^22+132x^23+647x^24+1140x^25+1408x^26+2820x^27+3248x^28+2780x^29+1492x^30+1132x^31+626x^32+156x^33+256x^34+12x^35+106x^36+6x^38+5x^40+1x^48

The gray image is a code over GF(2) with n=224, k=14 and d=80.
This code was found by Heurico 1.16 in 2.09 seconds.