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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+108x^77+291x^78+316x^79+564x^80+768x^81+672x^82+1028x^83+926x^84+1118x^85+660x^86+588x^87+400x^88+236x^89+170x^90+106x^91+84x^92+60x^93+59x^94+6x^95+4x^96+12x^97+2x^98+2x^99+2x^100+2x^101+2x^102+2x^103+2x^104+1x^128

The gray image is a code over GF(2) with n=672, k=13 and d=308.
This code was found by Heurico 1.16 in 2.35 seconds.