The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+212x^81+279x^82+710x^83+724x^84+1018x^85+821x^86+834x^87+786x^88+978x^89+711x^90+632x^91+212x^92+146x^93+27x^94+56x^95+2x^96+4x^97+14x^98+6x^99+4x^101+4x^102+1x^104+2x^105+4x^109+2x^111+1x^112+1x^120

The gray image is a code over GF(2) with n=696, k=13 and d=324.
This code was found by Heurico 1.16 in 95.5 seconds.