The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  8  1  1  0  1  2 12  1  8  1 12  2  1  1  8  1  2  0  0  2  1  2  1  0  1  1  2  1  1  1 12  1  1  2  4  1  4  1  1  2  1  1  8  2  1 12  1  4 12  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 14  0  4  2  6 12 10  8 10 10  2  8 12  4 10 12 12  0  6  2 12  6  0  4 14  4  2 10  2 10 12  6  2  0  2  4  4  0  4 10  2  4 14  2 10  4  6  4  4  6  2  0 14  4  8 10  4 12  4 10  4 12  2  8  4  2 14  4  2  2
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  8  4  2 14  6 14  4 14  8  8 10  8  2 12 10 10  4  4  6 12  2  2 10  2  8  4  6  0  2  0  4  4  0  0  6  4  6  2  2 12 12  6  2  2  6  2  2  2  4 14 14 12  6 12  2  6  4  8  2  4  8  6  2  6 14  8  8 12  4 12
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10 14 12  6 12 10  4  4 14  4 10  2  0  8  2  8  2 14  2  6  4  0  8  4  8 10  6 10  4 12  0  2  8  6 10 14  4  0  6  6 14  2 14 14  0  0 12  4 10  0  0  8  0  2  6  2  0  2  0 14 12 10 10  4  8  0 14  6  2  2  0
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  0  4  0  8  8  0  0  4 12 12 12  0  4 12  4  8  0  8  8  0  8  4 12  8  0  4  0  4 12 12  4  4  4  0  8  4  0  0  8  8  0  0  4  4  8  0  8 12  8  0  8  4  8 12 12  0  4 12  4  0 12  8  0  8  0  8  4  8 12

generates a code of length 87 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+157x^78+466x^79+670x^80+1020x^81+1306x^82+1942x^83+2445x^84+3068x^85+3728x^86+3590x^87+3706x^88+3192x^89+2320x^90+1626x^91+1175x^92+830x^93+515x^94+412x^95+235x^96+176x^97+93x^98+32x^99+20x^100+18x^101+6x^102+12x^103+2x^104+2x^106+2x^108+1x^122

The gray image is a code over GF(2) with n=696, k=15 and d=312.
This code was found by Heurico 1.16 in 27.1 seconds.