The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+51x^68+202x^69+281x^70+604x^71+1107x^72+1828x^73+2523x^74+3452x^75+4245x^76+4242x^77+4255x^78+3516x^79+2656x^80+1804x^81+901x^82+510x^83+221x^84+150x^85+76x^86+22x^87+30x^88+24x^89+20x^90+22x^91+6x^92+6x^93+6x^94+2x^95+2x^96+1x^100+2x^102

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 17.9 seconds.