The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+137x^20+16x^21+236x^22+208x^23+558x^24+1200x^25+1164x^26+2672x^27+3981x^28+2672x^29+1204x^30+1200x^31+571x^32+208x^33+196x^34+16x^35+119x^36+16x^38+6x^40+3x^44

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 2.07 seconds.