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

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

Homogenous weight enumerator: w(x)=1x^0+79x^76+4x^77+241x^78+112x^79+576x^80+448x^81+914x^82+1348x^83+1607x^84+2852x^85+2425x^86+4472x^87+2802x^88+4456x^89+2426x^90+2848x^91+1537x^92+1332x^93+856x^94+408x^95+453x^96+120x^97+215x^98+28x^99+83x^100+4x^101+73x^102+22x^104+12x^106+4x^108+5x^110+2x^112+1x^114+2x^116

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 34.3 seconds.