The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+186x^79+786x^80+2036x^81+2697x^82+4290x^83+4975x^84+6716x^85+7180x^86+8050x^87+7330x^88+6920x^89+5169x^90+4026x^91+2032x^92+1420x^93+814x^94+472x^95+156x^96+126x^97+72x^98+44x^99+13x^100+12x^101+4x^102+4x^103+1x^104+2x^105+2x^108

The gray image is a code over GF(2) with n=696, k=16 and d=316.
This code was found by Heurico 1.16 in 55.8 seconds.