The generator matrix

 1  0  1  1  1  6  1  4  1  1  2  1  1  8  1  1  8  1  6  1 10  1  1  1  1  1  0  6  1  1 10  1  1 12  1  8  1  1  1  1  1  1  1 12  1  1  1  1  0  0  2  1  1  2 14  6  4  1  1  1  0  1 10  1  1  2 12  1  1  1  1  4  1  1  2  2
 0  1  1  6  7  1  3  1  4  5  1  2  8  1  7 13  1  6  1  3  1 10  5  0 14  1  1  1 12 15  1 11  2  1 11  1  8  1  9  7 14  0 13  1 12 13 10 12  2  1  1  5  2  8  1  1  1  1 12 14  1  6  1  9  5 12  1 15  4 15 12  2  6 11  0 12
 0  0  2  0 14  0  0  6  2  8 14  6  0  8  6 10 10  4  2  4 12  2  4  6 14 10 14 10  0 10  8  4 12  8 10 12  4 12  6  2  6  6  4 10  0 14  0 14  2  4  6 10  2  2  4  6  6  2  0  8  0  2 14  6 12  6  2  6 14  0  2  2  4  4  6  2
 0  0  0 12  0  0  8 12  8  8 12 12 12  4 12  8  8 12  0 12 12  4 12  0  4 12  0 12  0 12  0  0  8 12  8  8  0 12  4  8  0 12  8  8 12  4  4 12 12  4  0 12  0  4  0  8 12  4 12  0  4 12  4  8  0  4  0 12  8  4 12  8  8  4  0  4
 0  0  0  0  8  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  8  8  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  8  8  8  8  0  8  0  0  0  8  8  8  8  8  8  0  8  0  0  0  0  8  0  8  8  8  8  0  0  8
 0  0  0  0  0  8  8  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  8  0  0  8  0  8  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  0  8  8  0  8  8  8  8  0  0  8  8  0  0  8  8  0  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+123x^68+328x^69+727x^70+1280x^71+1997x^72+2776x^73+3352x^74+3936x^75+4057x^76+3816x^77+3529x^78+2644x^79+1793x^80+1180x^81+509x^82+296x^83+176x^84+88x^85+58x^86+36x^87+34x^88+4x^89+15x^90+8x^92+2x^94+3x^96

The gray image is a code over GF(2) with n=608, k=15 and d=272.
This code was found by Heurico 1.16 in 16.5 seconds.