The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+89x^82+414x^83+486x^84+516x^85+394x^86+522x^87+376x^88+472x^89+282x^90+294x^91+94x^92+64x^93+37x^94+18x^95+6x^96+4x^97+8x^98+12x^100+4x^102+1x^106+1x^112+1x^118

The gray image is a code over GF(2) with n=696, k=12 and d=328.
This code was found by Heurico 1.16 in 0.865 seconds.