The generator matrix

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

generates a code of length 73 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+339x^68+56x^69+418x^70+296x^71+725x^72+568x^73+718x^74+312x^75+274x^76+48x^77+194x^78+86x^80+42x^82+14x^84+4x^86+1x^124

The gray image is a code over GF(2) with n=584, k=12 and d=272.
This code was found by Heurico 1.16 in 16.3 seconds.