The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12 12  2  4  1 12  4  1  2  1  2  2  2  2  1  1 12  2  1  1  1  1  2  8  1  1 12  1 12  1  1  4  4  1  1  1  2  8  8  1  4  1  2  2  0  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 14  0  4  2  6 12  8 14  4 14  4 12 10 10  2 12  2  2  2  6  0 12  8 14 12 12  4  2 14  4  8  2 10  4  4  2  4  2  8  4  0 12  6  4 10  6  8  2  2  6 14  8  2  0  4 12  4  8  6  2  0
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  8  4  2 14  6 14  4 12 14  0  6  4  2  2 12  2 10 10  0 14  2  8  6  6  0  2 10  8  0  2  0 12  8 12  4 14 12 14  4 14 10  8  8  2  2  6  2 14  8  6 14 10  6  0 12  2  4  2  6 12  8
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10 14 12  6 12 10  4 12  8  2 14  0 14 12 14  4 12 12 10  0  6  2  2 12 14  2 10  8  4 10 10  6  2  6 10 12  2  2 10  2  0 14  2  4 14  8  2  8  8  6 14  8  4  0  2  4 12 12 10  6  0  0
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  0  4  0  8  8 12  8  0  4 12  8  4 12 12  0  8  4  4  0 12  8  4  4  0  4 12 12  8  8 12  8  4  0  0 12  4  8  4  8  4  4 12 12  4 12 12  4  4  4  0  8  0  0  8 12 12  0  8 12  4

generates a code of length 78 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+104x^69+378x^70+732x^71+884x^72+1326x^73+1786x^74+2660x^75+2659x^76+4228x^77+3419x^78+4244x^79+2952x^80+2512x^81+1545x^82+1276x^83+761x^84+524x^85+293x^86+224x^87+116x^88+66x^89+33x^90+16x^91+16x^92+8x^93+2x^94+2x^96+1x^104

The gray image is a code over GF(2) with n=624, k=15 and d=276.
This code was found by Heurico 1.16 in 23.6 seconds.