The generator matrix

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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+816x^82+1774x^83+3343x^84+4228x^85+6104x^86+6106x^87+7052x^88+7318x^89+7689x^90+5890x^91+5551x^92+3696x^93+2710x^94+1410x^95+929x^96+434x^97+293x^98+96x^99+48x^100+16x^101+20x^102+4x^103+4x^104+4x^105

The gray image is a code over GF(2) with n=712, k=16 and d=328.
This code was found by Heurico 1.16 in 62.2 seconds.