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  2  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  2  4  1  1  2  4  1  1  4  1  1  2  0  1  4  1  1  1  8  1  1  0  2  1  4  1
 0 12  0  0  0  0  0  0  0  4 12 12  4 12  4 12  8 12  8 12  0  8 12  8  4 12 12  8  4  4 12  0  8 12  0  8  8  8  0  4  0 12  0  4  8  0  4 12  0  4 12  0  8  4 12  8  0  8 12  8  0  4 12  0  4 12 12  0  8  4  8 12  0  8  4  8  0  0
 0  0 12  0  0  8 12 12  4  4  4  8  4 12  0  8  0  8  0  4  4  4  4  4 12  0  8 12 12  0  8  8 12  0  0  8  8 12  0  0  8  4  0  0  8 12  4  8  8  4 12  4  4  4  8 12 12  0 12  0  0  4  0  0  8  8 12  4 12 12  8  4  8  4  8  0  8  0
 0  0  0 12  0 12 12  4  8  0  0  0  4 12  4  4  8 12  4  4  8  8  4  4  0  8  0  4  0  8  4  4 12  0  0  8  4 12  4 12  0  0  8  4  4 12  0  8  8 12  4  4  0  0  0 12  4  4  8 12  4  4  8  4  4  8  8  4  4  0  4  8  4  4  0 12  4  0
 0  0  0  0 12  4  8  4  4  0  4  4  4  0  8 12 12  8  8  4  8 12  0 12  4 12  8  0  0  0  4  4  8  4  8  0 12 12 12 12 12  0  4  0  8  4  4  0  4  8  4 12  8  0 12  0  4  8  4 12  4  0  0  0 12  8 12  4  4 12 12  4  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+46x^70+48x^71+82x^72+140x^73+210x^74+312x^75+453x^76+574x^77+546x^78+536x^79+403x^80+288x^81+153x^82+58x^83+91x^84+34x^85+21x^86+28x^87+14x^88+16x^89+13x^90+10x^91+11x^92+4x^93+2x^94+1x^100+1x^126

The gray image is a code over GF(2) with n=624, k=12 and d=280.
This code was found by Heurico 1.16 in 0.838 seconds.