The generator matrix

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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+225x^78+316x^79+664x^80+680x^81+919x^82+984x^83+897x^84+788x^85+776x^86+828x^87+610x^88+192x^89+177x^90+48x^91+47x^92+4x^93+9x^94+14x^96+6x^98+2x^100+4x^108+1x^112

The gray image is a code over GF(2) with n=672, k=13 and d=312.
This code was found by Heurico 1.16 in 1.91 seconds.