The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  8  1  1  1  6  1 10  1  1  1  4  1  1  1  8  1  2  1 14  1  1  1  1  0 10  1  1 12  1  6  1  1 10  0  1  1  1  6  1 14  1 10  1 14  1  1  8  1  1  1  1  1  1  1  1  1  1  1  1 14  1  2  1  2  1
 0  1 11  6 13  1  7  8  1 14  1  1  4  1 11  2 13  1  1  1  8  7  6  1  3 10 12  1  9  1 10  1  9  6  1 15  1  1  1  4  1  8  1  3  5  1  1  3  3 12  1  8  1 11  1  8  1  3 14  1 11  2  2 14 10  8 13  5  6 14 15  6  1 15  1 10  1  0
 0  0 12  0  4  0  4  4  0 12  4  8 12 12  8  0  8  4  8  4  8  0  0 12  8  4  4  0 12  4  0  0  8 12  8  8  4  8  4 12  4  0  0 12 12  0  4  8 12  0 12  0  0  4  0 12  4  8  4  4  4  4  0  4  8  4  0  0  8  0  4  8  4  0  8 12  4  0
 0  0  0 12  0  0  0  8  8  8  0  0  8  0 12  4  4  4  4  4  4 12  0  8  0 12 12 12  4  8  8  4  8 12  8  8 12 12 12  8  8 12  0 12 12 12  4  0  0  0 12  0  0 12  8 12 12  0  8  4 12  0  4  0 12  0  4  8  8  0  8 12  8  4  4 12  0  0
 0  0  0  0  8  0  8  8  8  0  0  8  0  0  8  8  0  8  0  0  8  8  8  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  8  0  8  8  0  8  0  0  0  0  8  8  8  0  0  8  8  8
 0  0  0  0  0  8  8  0  0  8  8  8  0  8  0  8  8  0  0  8  0  8  0  0  0  8  0  0  8  8  8  0  8  0  0  8  0  8  8  8  0  8  0  8  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  8  0  0  0  8  8  0  8  0  8  0  8  0  0  0  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+44x^70+156x^71+280x^72+560x^73+1106x^74+1128x^75+1946x^76+1772x^77+2530x^78+1768x^79+1927x^80+1090x^81+1064x^82+538x^83+231x^84+112x^85+42x^86+10x^87+18x^88+12x^89+8x^90+14x^91+10x^92+4x^93+4x^94+2x^95+2x^96+2x^97+1x^100+2x^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 4.85 seconds.