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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+251x^70+132x^71+388x^72+376x^73+839x^74+636x^75+1120x^76+784x^77+1170x^78+636x^79+718x^80+376x^81+409x^82+132x^83+114x^84+63x^86+16x^88+13x^90+6x^92+4x^94+4x^96+3x^98+1x^112

The gray image is a code over GF(2) with n=616, k=13 and d=280.
This code was found by Heurico 1.16 in 83.9 seconds.