The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+71x^68+428x^69+830x^70+1628x^71+2306x^72+4012x^73+4786x^74+6688x^75+7577x^76+8640x^77+7904x^78+7294x^79+4842x^80+3618x^81+1900x^82+1434x^83+738x^84+402x^85+163x^86+102x^87+69x^88+50x^89+28x^90+6x^91+6x^92+2x^93+2x^94+6x^96+2x^98+1x^102

The gray image is a code over GF(2) with n=616, k=16 and d=272.
This code was found by Heurico 1.16 in 59.7 seconds.