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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+35x^74+78x^75+151x^76+274x^77+377x^78+608x^79+733x^80+1514x^81+1426x^82+3128x^83+2177x^84+4616x^85+2533x^86+4634x^87+2280x^88+3184x^89+1403x^90+1546x^91+638x^92+590x^93+268x^94+208x^95+111x^96+54x^97+72x^98+32x^99+37x^100+8x^101+21x^102+6x^103+9x^104+8x^106+5x^108+1x^110+1x^112+1x^120

The gray image is a code over GF(2) with n=688, k=15 and d=296.
This code was found by Heurico 1.16 in 32.9 seconds.