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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+84x^68+420x^69+784x^70+1304x^71+1799x^72+2606x^73+3509x^74+4970x^75+5786x^76+7490x^77+7653x^78+7854x^79+6281x^80+5072x^81+3419x^82+2514x^83+1478x^84+972x^85+640x^86+396x^87+229x^88+124x^89+54x^90+48x^91+16x^92+18x^93+2x^94+2x^95+6x^96+2x^97+2x^98+1x^102

The gray image is a code over GF(2) with n=624, k=16 and d=272.
This code was found by Heurico 1.16 in 89.8 seconds.