The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  4  4  2  1  2  2  2
 0 12  0  0  0  0  0  0  0  0  0 12 12  4 12  8 12 12  4 12  8  4  8  0  0  8  0  8
 0  0 12  0  0  0  0  0  0  0  4  0  4 12 12  4  8  8  4  4  4  4  0  8 12  8  4  8
 0  0  0 12  0  0  0  4 12 12  4 12  0  8  4  4  4  8  8 12  4 12  4  0  8  8 12  0
 0  0  0  0 12  0  4  4  4  0  8  8  8  4  8 12  4  0  0  0  0  4  4 12  4  4 12  4
 0  0  0  0  0 12  4  8  4  4  0  0 12  4 12  8  0  4  0  8 12  8  4  4 12  8 12  4
 0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  8  8  0  0  8  0  8  8  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+170x^20+8x^21+690x^22+40x^23+1242x^24+856x^25+3924x^26+5240x^27+8310x^28+5240x^29+4064x^30+856x^31+1379x^32+40x^33+508x^34+8x^35+151x^36+30x^38+10x^40+1x^52

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 7.5 seconds.