The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+571x^24+160x^25+1388x^26+864x^27+2350x^28+864x^29+1224x^30+160x^31+523x^32+76x^34+10x^36+1x^40

The gray image is a code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 90.7 seconds.