The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+201x^78+488x^79+887x^80+1594x^81+2812x^82+3560x^83+5714x^84+5880x^85+8047x^86+7262x^87+8498x^88+6118x^89+5372x^90+3352x^91+2594x^92+1230x^93+771x^94+504x^95+282x^96+156x^97+88x^98+42x^99+37x^100+10x^101+19x^102+6x^103+2x^104+4x^105+1x^106+2x^107+1x^108+1x^114

The gray image is a code over GF(2) with n=696, k=16 and d=312.
This code was found by Heurico 1.16 in 69.8 seconds.