The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  1  2  1  4  1  1  1 10  1  0  1 14  1  1  1  1  1  4  1  6  1  1  1  1  1  2  1  1 12  1  1  1  1  6  1  4  1  4  6  1  1  1 10  4  1  2  1 10  4  1  8  1  1  1  8 12  1  1  1  1  1 14  8  2  2  1
 0  1  1  6  1  3  5  4  1  2  1  7  9  1  6  1  2 13  8  1  7  1  5  1 15 12 15 14  1  1  9  1 15  2  3  0  0  1 12 10  1 14 11  8  2  1 15  1  3  1  1  9  5 12  1  1  5  1  4  1  1  0  1 14  6  4  1  4  5 14 11 14 12  1  2  4 14  0
 0  0  2  0  0  8  8 10  6 10 14 10 14 10  6  4  4  4 10  0 12 12  4 10  8  0  6  2  2  2  8 12  2  2  4 12 14  2 14 14  0  0 12  0  8  6 14 12 10 10  0  8 10  4  4 10 12  2 12  6  6  0 14  4  4  2  4  2 14 10  4 10  4 14  2  6  2  0
 0  0  0  8  0  8  0  0  8  8  0  0  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  8  0  8  0  0  8  8  0  8  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  8  0  0  0  8  0  0  8  0  0  0  8  8  8  8  8  8  0
 0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  0  8  0  0  8  8  0  8  8  8  8  0  8  8  8  0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  8  8  8  0  8  0  0  8  0  0  0  0

generates a code of length 78 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+67x^72+446x^73+629x^74+800x^75+805x^76+996x^77+887x^78+1006x^79+863x^80+678x^81+441x^82+304x^83+94x^84+60x^85+28x^86+30x^87+8x^88+24x^89+9x^90+4x^91+1x^92+4x^93+5x^94+1x^98+1x^104

The gray image is a code over GF(2) with n=624, k=13 and d=288.
This code was found by Heurico 1.16 in 1.44 seconds.