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  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  2  1  1  1  2  1  1  1  2  1  1  4  1  2  1  1  1  1  4  1  1  1  4  1  1  1  1  2  2  1  1  4  2  1  4  1  0  1  0  0  2  1  2  2  0  2  1  1  1  1  1  2  2  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  4  8  4 12 12  8  8 12  0  4  8  0  4  0 12  4  4  0  0  4 12  0  4  8  8  8 12  8  8  8  0  4  4  0  8  4  8  4 12  0 12  8  0  0 12  4  0  0  4  8  8  4  0  4  8 12  4 12  4 12  0 12 12  8 12  0  8  4  4 12 12  4  0 12  4 12  8  4  4  4  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  4 12  8 12  0  8  4  8  8  8  8  4  4 12 12 12 12 12  4  0  0  8  4  4 12  4 12  0  8  4 12  0  0  8  4 12 12 12  8  4  0  8  4 12  0  8  0  0  0  4  8 12 12 12 12 12  0  0  0  0  8  0 12  0  8  4  8 12  4  4  8  8  8  0  4  0  4  8  8  4  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  8  4  0  4  4 12  0  0  4  0  0  8 12  4  4  8  8 12 12  0  4  0  0 12 12  0  8  4 12  8  0 12 12 12  8  8 12  8  0  0  8  0  0  4 12  4 12 12  4  0 12  4  8  0  4  4  0  4  4  8  8  8  0  4  4  8  4  8 12  0  0  0 12  0  4  0  4 12 12  8  0
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  8  8  8  8  8  0  8  8  8  0  0  0  0  8  0  0  0  8  8  8  0  0  8  8  0  0  0  8  8  0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  8  0  8  8  0  8  8  0  8  8  8  8  8  0  8  8  8  8  8  8  0  0  8  8  0  8  0  8  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  0  0  8  0  8  8  0  0  8  0  8  0  0  0  0  0  0  8  8  0  8  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  8  0  8  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  8  0  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  8  8  0  8  0  0  8  8  0  0  8  0  8  0  0  0  0  0  8  0  8  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  8  8  8  0  8  0  8  0  0  0  8  8  0  8  8  8  8  0  8  8  8  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0  0  0  8  8  0  8  8  8  0  8  0  8  8  0  8  8  8  8  0  0  0  8  8  8  0  0  0  8  0  0  8  8  8  0  8  0  0  0  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  8  8  8  8  8  0  8

generates a code of length 98 over Z16 who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+46x^86+82x^87+129x^88+194x^89+205x^90+286x^91+374x^92+460x^93+730x^94+1156x^95+1588x^96+1948x^97+2144x^98+1974x^99+1616x^100+1170x^101+705x^102+416x^103+247x^104+210x^105+167x^106+120x^107+76x^108+86x^109+74x^110+50x^111+57x^112+22x^113+19x^114+12x^115+6x^116+4x^117+5x^118+2x^120+2x^121+1x^146

The gray image is a code over GF(2) with n=784, k=14 and d=344.
This code was found by Heurico 1.16 in 13.7 seconds.