The generator matrix

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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+84x^69+743x^70+1160x^71+2433x^72+2776x^73+3754x^74+3528x^75+4292x^76+3616x^77+3886x^78+2324x^79+1867x^80+1036x^81+646x^82+256x^83+210x^84+36x^85+55x^86+28x^87+23x^88+4x^89+4x^90+6x^92

The gray image is a code over GF(2) with n=608, k=15 and d=276.
This code was found by Heurico 1.16 in 12.6 seconds.