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

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

Homogenous weight enumerator: w(x)=1x^0+70x^68+450x^69+607x^70+984x^71+1382x^72+1922x^73+2547x^74+3056x^75+3684x^76+3700x^77+3718x^78+3088x^79+2370x^80+1792x^81+1240x^82+836x^83+480x^84+384x^85+211x^86+122x^87+42x^88+34x^89+25x^90+8x^91+2x^92+6x^93+4x^94+2x^95+1x^96

The gray image is a code over GF(2) with n=616, k=15 and d=272.
This code was found by Heurico 1.16 in 23.1 seconds.