The generator matrix

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

generates a code of length 74 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+49x^68+356x^69+622x^70+750x^71+931x^72+1158x^73+774x^74+1050x^75+851x^76+728x^77+449x^78+178x^79+111x^80+86x^81+13x^82+34x^83+24x^84+4x^85+12x^86+4x^87+4x^89+1x^90+1x^96+1x^102

The gray image is a code over GF(2) with n=592, k=13 and d=272.
This code was found by Heurico 1.16 in 1.23 seconds.