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  4  1 12  1  1  2 12  2  2  2 12  8  8  1  1  2  2  2  8  1  0  1  0  2 12  2  1 12  1  1  8  0  1  1  2  1  8  2  2  1  1  2  1  1
 0  2  0  0  0  0  0  0  0 10  6 10 14 10  2  2  8  4 12  8  6  6 10  2  4  6  4  2 10  4  0 14 12  8  2  6  2  4 12 10 12 10  0 14  2  2  4  4  6  6  0 12  2  4  4  8 12 14  2 10 14  2  4 10  2  8  4  6  8  6  2  8 10 14 12 14  8  8
 0  0  2  0  0  8 10  6  6  2  6  0  2  0  8 14 10  0  8  2 14 12  4  8  2  8 12  6  2  0  6  6 10 12  4 14  8  4  6 12  2  4  8  2  4  6  4  4 12  2  2  6  8  2  2  0  2  8  4 12  2  6  2  2 12  2 12  0 12 14 10 14  4 10  8  8  2  8
 0  0  0  2  0 10 10 10  8  2 14  8  4 10 10  8 14 10  8 12  2  0 14  0 14  6 12  8  2  2  4  4 12  0 14 14 12  0  0  4 10 14  6  2  4 10  2 10  0  4 12 14  6  8  2 14  4  2 14 10  0  4 14 14  8  2 10 12 10  0  8  0  4  8 14 12  8  8
 0  0  0  0  2  2  8 10  2 14  8 14  2  2  4 12 12 10  2  6 10  8 12  2 14  2  0 10  4 12  0  4  4  0  0  4  4  6 14  0  6 10  2  4 14 10 12  2  4 14  6  0 10  4  0  0  8  0  2  8  2  8 10  8 14 10  4  2  4  6 14  2  8 14 10  6 14  8

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

Homogenous weight enumerator: w(x)=1x^0+42x^68+390x^69+800x^70+1308x^71+1719x^72+2744x^73+3607x^74+4850x^75+6288x^76+7452x^77+7516x^78+7246x^79+6316x^80+5158x^81+3388x^82+2434x^83+1640x^84+1132x^85+704x^86+390x^87+172x^88+140x^89+41x^90+12x^91+12x^92+22x^93+5x^94+2x^96+2x^97+2x^98+1x^102

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 86 seconds.