The generator matrix

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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+57x^68+154x^69+260x^70+456x^71+770x^72+1430x^73+2204x^74+3812x^75+5303x^76+6296x^77+7985x^78+8442x^79+7904x^80+6522x^81+4905x^82+3604x^83+2169x^84+1434x^85+823x^86+460x^87+223x^88+70x^89+82x^90+48x^91+35x^92+28x^93+28x^94+10x^95+17x^96+2x^97+1x^104+1x^106

The gray image is a code over GF(2) with n=632, k=16 and d=272.
This code was found by Heurico 1.16 in 69.4 seconds.