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

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

Homogenous weight enumerator: w(x)=1x^0+68x^69+373x^70+588x^71+1196x^72+1228x^73+2076x^74+2420x^75+3608x^76+3364x^77+3507x^78+3620x^79+3060x^80+2196x^81+1989x^82+1212x^83+904x^84+456x^85+459x^86+144x^87+168x^88+48x^89+38x^90+16x^91+16x^92+5x^94+7x^96+1x^98

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 23.4 seconds.