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  8  2 12  2  2  2  1  4  1  1  1  1  8  2  1 12  1  1  0  2  8  1  1  2  2  1  1  2 12  2  1  1  1  1  1  2  8  1  1  1  4  1  1  1 12  1  1  2
 0  2  0  2  0  0  2 10  8  0  6  6  4  2  2 12  0 12  6 14 10  8 12 14  8  0  6  8 10 12  4  2 10 14 10  2  2  6  2  6  8  4 12 12  8  8  6  2  6  2 14  6  2  4  8 14  2  2 14  0  4  4  2 10 14  2 14  8  0  8 10 14 12  2 10  6 12
 0  0  2  2  0  6 10  8  6  4  6 12 12 12 14  2  4 14  8 10  4 10  8  6 12  6  8  2 14  2 10  6 14  0  0 14  8  0  2  8 10  2  2  8  2  4  4 14 12  4 10 10  4  2 10  8  0  8 10 12 14 10  6 14  4 10  2 12  2  2  4  2  2 12  6  2 10
 0  0  0  4  0  0  4  0  0  0 12  0  0  0  4  8  0  8  8  4  8  8  0  4  8  8  8  0 12  8  8 12  4  0  8  0  8  4  0  4 12  4  4 12 12  4 12  0  0 12  8  8 12  4 12 12 12  8  0  4 12  0  8 12  8  4  4 12  4  8 12 12  0  0  4  8  8
 0  0  0  0 12  0 12  4  4  4 12  4  8  0  8 12  8 12  0  8  4  8 12  0  0  8  4  4  4  8 12 12 12  4  8  0  4  0  4 12  0  0  4  8 12  8  8  0  4  0  8 12  0 12 12  4  0  0 12  4  8  4  0  8  4  4  8  8  4 12  8  4 12  0  0  4  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  8  8  0  8  0  8  8  0  8  0  0  8  0  0  8  8  0  8  0  8  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  8  8  8  0  0  8  0  8  0  8  8  8  0  8  8  0  8  0  0  8  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+194x^68+224x^69+672x^70+704x^71+1333x^72+1884x^73+2368x^74+3576x^75+3245x^76+4676x^77+3254x^78+3672x^79+2222x^80+1768x^81+1154x^82+604x^83+515x^84+196x^85+208x^86+80x^87+116x^88+20x^89+50x^90+4x^91+21x^92+6x^94+1x^108

The gray image is a code over GF(2) with n=616, k=15 and d=272.
This code was found by Heurico 1.16 in 25.5 seconds.