The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+49x^78+354x^79+926x^80+1760x^81+2805x^82+3954x^83+5399x^84+6078x^85+7858x^86+7578x^87+7533x^88+6124x^89+5729x^90+3956x^91+2506x^92+1362x^93+708x^94+420x^95+178x^96+114x^97+52x^98+16x^99+26x^100+16x^101+11x^102+8x^103+6x^104+2x^105+2x^106+2x^107+1x^108+2x^110

The gray image is a code over GF(2) with n=696, k=16 and d=312.
This code was found by Heurico 1.16 in 56.9 seconds.