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

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

Homogenous weight enumerator: w(x)=1x^0+44x^74+50x^75+141x^76+122x^77+275x^78+250x^79+314x^80+578x^81+609x^82+1222x^83+1554x^84+1912x^85+2399x^86+1898x^87+1610x^88+1200x^89+515x^90+538x^91+316x^92+214x^93+164x^94+106x^95+106x^96+62x^97+62x^98+30x^99+42x^100+8x^101+15x^102+2x^103+8x^104+8x^106+3x^108+3x^110+1x^112+1x^114+1x^122

The gray image is a code over GF(2) with n=688, k=14 and d=296.
This code was found by Heurico 1.16 in 11.7 seconds.