The generator matrix

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

generates a code of length 88 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+22x^76+26x^77+52x^78+98x^79+237x^80+414x^81+556x^82+1374x^83+1322x^84+3288x^85+2212x^86+5552x^87+2533x^88+5552x^89+2216x^90+3288x^91+1281x^92+1374x^93+528x^94+414x^95+201x^96+98x^97+38x^98+26x^99+18x^100+13x^102+10x^104+8x^106+3x^108+2x^110+1x^112+6x^114+2x^116+1x^118+1x^120

The gray image is a code over GF(2) with n=704, k=15 and d=304.
This code was found by Heurico 1.16 in 20.9 seconds.