The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+232x^70+560x^71+1552x^72+2172x^73+4557x^74+4960x^75+7565x^76+6728x^77+9475x^78+6836x^79+7581x^80+4588x^81+3844x^82+2136x^83+1495x^84+576x^85+399x^86+100x^87+85x^88+16x^89+42x^90+22x^92+10x^94+1x^96+1x^98+2x^100

The gray image is a code over GF(2) with n=624, k=16 and d=280.
This code was found by Heurico 1.16 in 50.2 seconds.