The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+68x^69+173x^70+416x^71+746x^72+1090x^73+1631x^74+2752x^75+3454x^76+3954x^77+4450x^78+3872x^79+3379x^80+2648x^81+1772x^82+1150x^83+558x^84+280x^85+126x^86+70x^87+40x^88+46x^89+30x^90+26x^91+8x^92+10x^93+6x^94+2x^95+6x^96+2x^98+1x^102+1x^106

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 18.2 seconds.