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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+140x^77+116x^78+262x^79+328x^80+444x^81+446x^82+716x^83+582x^84+404x^85+167x^86+144x^87+93x^88+116x^89+36x^90+56x^91+13x^92+16x^93+1x^94+2x^95+6x^96+1x^98+4x^99+1x^100+1x^138

The gray image is a code over GF(2) with n=664, k=12 and d=308.
This code was found by Heurico 1.16 in 9.86 seconds.