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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+51x^68+88x^69+144x^70+238x^71+230x^72+292x^73+377x^74+500x^75+854x^76+1398x^77+2451x^78+3198x^79+2541x^80+1452x^81+819x^82+472x^83+291x^84+248x^85+185x^86+138x^87+118x^88+80x^89+71x^90+52x^91+40x^92+26x^93+12x^94+10x^95+2x^96+4x^98+1x^122

The gray image is a code over GF(2) with n=632, k=14 and d=272.
This code was found by Heurico 1.16 in 9.7 seconds.