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

generates a code of length 65 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+74x^57+170x^58+424x^59+600x^60+776x^61+1211x^62+1910x^63+1881x^64+2470x^65+1951x^66+1862x^67+1189x^68+650x^69+417x^70+362x^71+143x^72+120x^73+83x^74+42x^75+23x^76+6x^77+8x^78+8x^79+2x^80+1x^96

The gray image is a code over GF(2) with n=520, k=14 and d=228.
This code was found by Heurico 1.16 in 5.25 seconds.