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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+62x^70+266x^71+507x^72+1006x^73+849x^74+1340x^75+1630x^76+1870x^77+1788x^78+1818x^79+1502x^80+1342x^81+743x^82+552x^83+370x^84+282x^85+154x^86+160x^87+52x^88+60x^89+13x^90+8x^91+6x^94+2x^100+1x^106

The gray image is a code over GF(2) with n=624, k=14 and d=280.
This code was found by Heurico 1.16 in 6.34 seconds.