The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+127x^78+96x^79+558x^80+516x^81+1393x^82+1840x^83+2645x^84+3412x^85+4125x^86+3740x^87+4056x^88+3232x^89+2587x^90+1864x^91+1220x^92+580x^93+378x^94+76x^95+133x^96+4x^97+98x^98+42x^100+18x^102+14x^104+10x^106+2x^112+1x^116

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 21.1 seconds.