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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+96x^62+64x^63+372x^64+324x^65+613x^66+928x^67+1186x^68+1668x^69+1977x^70+2184x^71+1835x^72+1780x^73+1068x^74+848x^75+557x^76+316x^77+253x^78+72x^79+110x^80+8x^81+72x^82+28x^84+14x^86+6x^88+3x^90+1x^100

The gray image is a code over GF(2) with n=568, k=14 and d=248.
This code was found by Heurico 1.16 in 6.91 seconds.