The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+100x^72+652x^73+978x^74+1306x^75+1028x^76+1128x^77+734x^78+588x^79+476x^80+512x^81+248x^82+198x^83+109x^84+76x^85+30x^86+20x^87+4x^88+2x^90+1x^92+1x^96

The gray image is a code over GF(2) with n=616, k=13 and d=288.
This code was found by Heurico 1.16 in 1.03 seconds.