The generator matrix

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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+49x^68+174x^69+456x^70+794x^71+1818x^72+1962x^73+4436x^74+4134x^75+7791x^76+6212x^77+9947x^78+6380x^79+7940x^80+4184x^81+4175x^82+1898x^83+1624x^84+596x^85+472x^86+196x^87+115x^88+44x^89+54x^90+32x^91+14x^92+10x^93+9x^94+6x^95+6x^96+2x^97+3x^98+2x^100

The gray image is a code over GF(2) with n=624, k=16 and d=272.
This code was found by Heurico 1.16 in 63.2 seconds.