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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+58x^76+130x^77+238x^78+394x^79+433x^80+598x^81+840x^82+966x^83+1007x^84+958x^85+848x^86+594x^87+410x^88+286x^89+155x^90+110x^91+58x^92+28x^93+21x^94+8x^95+6x^96+12x^97+8x^98+4x^99+7x^100+4x^101+4x^103+2x^104+1x^106+2x^108+1x^126

The gray image is a code over GF(2) with n=672, k=13 and d=304.
This code was found by Heurico 1.16 in 2.39 seconds.