The generator matrix

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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+90x^69+253x^70+714x^71+1187x^72+2048x^73+2756x^74+3564x^75+3801x^76+4310x^77+3984x^78+3478x^79+2394x^80+1840x^81+1091x^82+550x^83+286x^84+196x^85+68x^86+80x^87+40x^88+12x^89+6x^90+14x^91+3x^92+1x^102+1x^106

The gray image is a code over GF(2) with n=616, k=15 and d=276.
This code was found by Heurico 1.16 in 15.7 seconds.