The generator matrix

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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+152x^78+698x^79+978x^80+1232x^81+1001x^82+990x^83+797x^84+854x^85+406x^86+316x^87+238x^88+198x^89+154x^90+100x^91+33x^92+20x^93+13x^94+8x^95+1x^96+1x^102+1x^106

The gray image is a code over GF(2) with n=664, k=13 and d=312.
This code was found by Heurico 1.16 in 1.15 seconds.