The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+100x^69+389x^70+558x^71+1362x^72+1772x^73+2694x^74+3404x^75+4472x^76+3946x^77+4177x^78+3270x^79+2604x^80+1522x^81+1203x^82+574x^83+336x^84+126x^85+94x^86+60x^87+46x^88+18x^89+14x^90+6x^91+8x^92+4x^93+3x^94+3x^96+1x^98+1x^102

The gray image is a code over GF(2) with n=616, k=15 and d=276.
This code was found by Heurico 1.16 in 16.7 seconds.