The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  0  1  1  8  2  1  2  1  1  1  0  4  1
 0  2  0  2  0 10 12 14  4  4  6  6 10  2  6  0  0 12  2  2  8  6  2 10  6  2  0  0
 0  0  2  2 12 14  6  4  4  2  6  0  6  0  0  2  6  0  4  2  2  6  8  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  0  8  8  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  0  0  8  0  0  0  8  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  0  8  0  8  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  0  8  0  0  8  8  0  0  0  8  0
 0  0  0  0  0  0  0  8  8  8  0  0  0  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+62x^20+90x^21+374x^22+350x^23+1177x^24+1760x^25+2948x^26+5964x^27+7268x^28+6012x^29+2976x^30+1808x^31+1141x^32+320x^33+348x^34+68x^35+70x^36+10x^37+10x^38+2x^39+9x^40

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 5.11 seconds.