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

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

Homogenous weight enumerator: w(x)=1x^0+62x^68+392x^69+562x^70+1174x^71+1067x^72+2024x^73+2183x^74+3462x^75+3340x^76+4400x^77+3499x^78+3628x^79+1998x^80+1884x^81+926x^82+942x^83+434x^84+336x^85+176x^86+124x^87+68x^88+52x^89+11x^90+12x^91+4x^92+3x^94+2x^95+1x^96+1x^104

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 seconds.