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

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

Homogenous weight enumerator: w(x)=1x^0+20x^86+42x^87+62x^88+158x^89+207x^90+294x^91+301x^92+642x^93+696x^94+1396x^95+1451x^96+2076x^97+1782x^98+2076x^99+1434x^100+1396x^101+669x^102+642x^103+262x^104+294x^105+169x^106+158x^107+44x^108+42x^109+16x^110+12x^112+16x^114+10x^116+5x^118+3x^120+2x^122+3x^124+2x^126+1x^152

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 11.1 seconds.