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

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

Homogenous weight enumerator: w(x)=1x^0+128x^70+224x^71+531x^72+568x^73+1096x^74+1164x^75+1754x^76+1956x^77+2079x^78+1900x^79+1447x^80+1104x^81+944x^82+488x^83+389x^84+180x^85+188x^86+60x^87+90x^88+32x^89+36x^90+4x^91+9x^92+9x^94+2x^96+1x^112

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 6.94 seconds.