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

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

Homogenous weight enumerator: w(x)=1x^0+32x^70+126x^71+212x^72+332x^73+428x^74+872x^75+514x^76+1268x^77+768x^78+1264x^79+494x^80+816x^81+379x^82+300x^83+166x^84+94x^85+36x^86+12x^87+15x^88+16x^89+13x^90+16x^91+3x^92+2x^93+7x^94+2x^95+2x^96+1x^102+1x^116

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 2.2 seconds.