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  1  2  1  2  1  1  1  1  1  1  1  2  1  2  1  2  1  4  1  1  1  2  1  1  1  2  2  1  1  1  0  1  4  1  0  1  2  1  2  1  4  4  2  1  1  4  2
 0 12  0  0  0  0  0  0  0  4 12 12  4  8  4  8  4 12 12  0  8 12 12  4  0  4 12  4  0  0  4  8  4  8  0 12 12  4  4  4  8  0  8 12 12 12  8  4  0  8  0  0  4  8 12 12  8  0  8 12  4  8  0 12 12  4  0  8  4  4  4  0  0  0  8 12  8  4 12
 0  0 12  0  0  0  4 12 12  4  4  0  8  0  4  8  8  8  4  4 12 12  8  4 12  8 12  0  0  8  4 12  0  8  4  8  4 12 12  8  4  8  8  4  4  8  8  8  4  8  8 12  8 12  0 12 12 12  4  8  8  8  4  4  4  8  0  0  4  8  0  8  8  8  0  4 12  4  4
 0  0  0 12  0  4  4  4  0  8  0  8 12  0  4 12  8 12 12  8  4 12  8  8 12  4  0 12  0 12 12  8 12 12  8  0  4 12  4  0  0 12  0  4 12  0  0  8 12  4  0  8 12  0  0 12  8 12  0  0  0  8  0  4 12  8  4 12 12  8  4  8 12  4 12  8  8 12  4
 0  0  0  0 12  4  8  4  4  0  4  4  0  0 12  8  8  4  0  8 12  8  4  0  8  0  4 12 12 12  4  4  4  0  4  0  4  0  4 12  0  4  8  8  4  0 12 12  8 12  8 12  8 12 12  0  0  4  4 12  8  0  0  0  0  4  0  4 12  8  8  0 12  8 12  0  0 12  8
 0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0  0  0  0  8  8  8  0  8  8  0  0  0  0  0  0  0  8  8  0  0  8  0  8  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  0  0  8  8  0  8  0  8

generates a code of length 79 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+100x^70+4x^71+308x^72+56x^73+336x^74+204x^75+680x^76+728x^77+1222x^78+1092x^79+1199x^80+712x^81+612x^82+228x^83+288x^84+40x^85+144x^86+8x^87+104x^88+52x^90+38x^92+30x^94+2x^96+2x^100+1x^104+1x^120

The gray image is a code over GF(2) with n=632, k=13 and d=280.
This code was found by Heurico 1.16 in 2.62 seconds.