The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+141x^20+16x^21+262x^22+320x^23+1122x^24+1808x^25+2540x^26+6016x^27+8219x^28+6064x^29+2584x^30+1856x^31+1139x^32+304x^33+244x^34+119x^36+2x^38+10x^40+1x^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 5.78 seconds.