The generator matrix

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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+207x^80+820x^81+1570x^82+2392x^83+2665x^84+3736x^85+3424x^86+4100x^87+3420x^88+3244x^89+2296x^90+2040x^91+1218x^92+772x^93+416x^94+220x^95+88x^96+56x^97+34x^98+16x^99+9x^100+12x^101+2x^102+8x^104+2x^110

The gray image is a code over GF(2) with n=696, k=15 and d=320.
This code was found by Heurico 1.16 in 15.1 seconds.