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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+63x^72+48x^73+186x^74+266x^75+284x^76+472x^77+516x^78+540x^79+522x^80+446x^81+247x^82+172x^83+117x^84+78x^85+65x^86+12x^87+30x^88+10x^89+7x^90+2x^91+7x^92+2x^93+2x^94+1x^126

The gray image is a code over GF(2) with n=632, k=12 and d=288.
This code was found by Heurico 1.16 in 1.01 seconds.