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

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

Homogenous weight enumerator: w(x)=1x^0+66x^72+224x^73+377x^74+566x^75+600x^76+866x^77+964x^78+1218x^79+917x^80+780x^81+512x^82+420x^83+214x^84+152x^85+96x^86+80x^87+43x^88+20x^89+35x^90+14x^91+14x^92+6x^93+6x^95+1x^120

The gray image is a code over GF(2) with n=632, k=13 and d=288.
This code was found by Heurico 1.16 in 1.88 seconds.