The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+232x^20+4x^21+564x^22+76x^23+1251x^24+516x^25+2430x^26+5548x^27+11445x^28+5548x^29+2542x^30+516x^31+1327x^32+76x^33+442x^34+4x^35+200x^36+38x^38+5x^40+3x^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 64.8 seconds.