The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+55x^64+14x^65+46x^66+54x^67+306x^68+176x^69+592x^70+462x^71+1455x^72+1122x^73+3133x^74+2556x^75+4697x^76+3520x^77+4682x^78+2556x^79+3128x^80+1122x^81+1449x^82+462x^83+529x^84+176x^85+246x^86+54x^87+44x^88+14x^89+49x^90+19x^92+30x^94+4x^96+9x^98+1x^100+2x^102+1x^104+2x^106

The gray image is a code over GF(2) with n=616, k=15 and d=256.
This code was found by Heurico 1.16 in 28.3 seconds.