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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+102x^68+4x^69+269x^70+36x^71+344x^72+260x^73+732x^74+680x^75+1137x^76+1088x^77+1326x^78+756x^79+559x^80+180x^81+259x^82+64x^83+160x^84+4x^85+102x^86+83x^88+25x^90+13x^92+7x^94+1x^120

The gray image is a code over GF(2) with n=616, k=13 and d=272.
This code was found by Heurico 1.16 in 2.5 seconds.