The generator matrix

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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+79x^68+678x^69+1552x^70+2460x^71+4164x^72+5572x^73+6258x^74+8154x^75+8069x^76+7936x^77+6944x^78+5336x^79+3524x^80+2322x^81+1173x^82+612x^83+402x^84+146x^85+71x^86+44x^87+15x^88+16x^89+1x^90+2x^91+2x^92+1x^94+2x^97

The gray image is a code over GF(2) with n=608, k=16 and d=272.
This code was found by Heurico 1.16 in 47.3 seconds.