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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+70x^61+130x^62+218x^63+281x^64+360x^65+457x^66+760x^67+1061x^68+1578x^69+2222x^70+2274x^71+2210x^72+1668x^73+1069x^74+644x^75+362x^76+318x^77+157x^78+136x^79+117x^80+84x^81+80x^82+58x^83+29x^84+18x^85+11x^86+4x^87+2x^88+2x^90+2x^91+1x^96

The gray image is a code over GF(2) with n=568, k=14 and d=244.
This code was found by Heurico 1.16 in 9.45 seconds.