The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  1  2  1  4  1  1  1  1  0 14  1  1  8  1  1  1  1  1 14  2  1  1 10  8  8  1  1  1  1  1  1  1  1  1 14  1 10  1 12  2  1  1  6 12  1  1  1  2  1  1  4  1  0  1  1  1  4  8  1  4  2  1  1 10  1  1  1  1 14  1
 0  1  1  6  1  3  5  4  1  2  1  7  9  1  6  1  2 11 12  3  1  1 12  1  1 14  3  0 15 12  1  1 14  7  1  1  1  3  1 13  6  9  2  7  8  1  1 15  1 12  1 14  9  8  1  1 13 11  1  8  3  5  2  7  8 11 14  4  1  1  5  2  0 10  6  1  8 15 11 10  1  0
 0  0  2  0  0  8  8 10  6 10 14 10 14 10  6  4  4 12  4 14 14  2 14  4  4  4  2  2  6  0 12 14 10  4  0 10  8  4  6  4 14  8  8  2 10 10  4  0  6 12  2  2  8  6  2  2 10 10  2 14  0  4 10 14  2  2  6  2 12 12  6 14  2  4 12  0  4 12 12  0 14  0
 0  0  0  8  0  8  0  0  8  8  0  0  8  0  0  8  8  0  0  0  8  8  0  0  8  8  8  0  8  0  0  0  8  8  8  8  0  8  8  0  0  8  0  0  8  0  8  8  0  8  8  0  8  8  0  0  8  0  8  8  0  8  0  0  0  8  8  8  0  8  8  8  0  0  0  0  0  8  0  0  0  0
 0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0  8  0  0  0  8  0  0  8  8  8  0  8  0  0  8  8  8  0  8  0  0  0  8  8  0  0  8  0  0  8  8  8  8  8  0  8  0  0  8  0  8  0  0  0

generates a code of length 82 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+77x^76+438x^77+672x^78+786x^79+932x^80+838x^81+1127x^82+832x^83+711x^84+600x^85+475x^86+366x^87+106x^88+66x^89+80x^90+16x^91+24x^92+10x^93+13x^94+16x^95+4x^96+1x^104+1x^106

The gray image is a code over GF(2) with n=656, k=13 and d=304.
This code was found by Heurico 1.16 in 1.56 seconds.