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  2  1  1  1  1  2  1  1  2  2  2  1  1  1  4  2  1  1  1  1  1  0  1  1  1  4  1  1  1  0  1  2  4  1  1  1  2  1  0  1  1  2  2  1  1  2  1  4  1  1  4  2  1
 0 12  0 12  0 12  0 12  0 12  8  4  0 12  0  8 12  4  0  8 12  4  0 12 12 12  4 12 12 12  8  8 12 12 12  0  0  8 12 12  0  0 12  8  4  4 12  0  0 12  4 12  8  4 12 12 12  0  0 12 12  8  4  4  0  0  4  0  8 12  4  0 12  4 12  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  0  0  8  0  0  0  8  8  8  8  8  0  0  8  8  8  8  0  0  8  8  0  8  0  0  8  0  0  8  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  0  8  0  8  0  8  0  0  8  8  8  8  8  0  0  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  8  8  8  8  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  0  8  0  0  8  0  8  8  0  0  0  8  0  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0  0  0  8  0  0  8  8  0  8  8  8  8  0  0  0  0  8  8  0  8  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  0  8  8  0  0  0  0  0  0  8  8  0  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  8  8  0  8  8  8  8  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  8  8  0  0  0  8  8  8  0  8  0  8  0  0  0  0  8  0  8  0  8  8  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  0  0  0  8  8  8  0  8  8  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  8  0  0  8  0  8  0  0  8  0  8  0
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  0  0  8  0  8  8  0  8  0  8  0  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  8  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  0  0  8  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  8  0  0  0  8  8  0  0  8  0  0  0  0  0  8  0  0  8  0  0  8  0  8  8  0  0  8  0  8  0  8  8  8  8  8  0  0  8  0  8  8  0  8  0  8  0  8  0  0  0  8  0  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+64x^64+14x^65+73x^66+54x^67+180x^68+126x^69+230x^70+212x^71+377x^72+700x^73+1031x^74+1830x^75+2172x^76+2396x^77+2193x^78+1688x^79+1022x^80+742x^81+353x^82+258x^83+177x^84+102x^85+122x^86+52x^87+81x^88+16x^89+51x^90+2x^91+14x^92+29x^94+7x^96+11x^98+1x^100+2x^102+1x^114

The gray image is a code over GF(2) with n=616, k=14 and d=256.
This code was found by Heurico 1.16 in 10.5 seconds.