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

generates a code of length 85 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+117x^76+12x^77+280x^78+28x^79+382x^80+252x^81+656x^82+700x^83+1241x^84+1092x^85+1172x^86+660x^87+604x^88+308x^89+276x^90+20x^91+156x^92+86x^94+64x^96+40x^98+22x^100+18x^102+4x^104+1x^136

The gray image is a code over GF(2) with n=680, k=13 and d=304.
This code was found by Heurico 1.16 in 2.91 seconds.