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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+34x^70+110x^71+211x^72+272x^73+506x^74+424x^75+1145x^76+774x^77+1388x^78+752x^79+1133x^80+384x^81+462x^82+226x^83+170x^84+80x^85+22x^86+14x^87+23x^88+18x^89+12x^90+10x^91+1x^92+6x^93+7x^94+4x^96+2x^97+1x^126

The gray image is a code over GF(2) with n=624, k=13 and d=280.
This code was found by Heurico 1.16 in 2.03 seconds.