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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+110x^70+60x^71+394x^72+360x^73+804x^74+660x^75+1470x^76+1532x^77+1888x^78+1908x^79+2121x^80+1532x^81+1224x^82+812x^83+620x^84+212x^85+318x^86+80x^87+111x^88+12x^89+74x^90+36x^92+24x^94+13x^96+6x^98+1x^100+1x^108

The gray image is a code over GF(2) with n=632, k=14 and d=280.
This code was found by Heurico 1.16 in 8.01 seconds.