The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  4  1  0  2  1  1  4  1  2  1  1  2
 0 12  0 12  0 12  0 12  0  4  8 12 12 12 12  4 12  0  4 12  0  8 12  0 12 12  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8
 0  0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  8  8  0  8  8  0  0  8  0  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+72x^20+80x^22+403x^24+128x^25+1072x^26+1408x^27+1864x^28+1408x^29+1072x^30+128x^31+406x^32+80x^34+64x^36+5x^40+1x^48

The gray image is a code over GF(2) with n=224, k=13 and d=80.
This code was found by Heurico 1.16 in 6.24 seconds.