The generator matrix

 1  0  0  1  1  1  2 10  1 14  1  1  4  1  1  1  8 12  0  1  1  1  6  1  1  1 12 14  1  1 14  1  6  4  1  8  1  1  6 10 14  1  8  1  1  1  1 14  0  1  1 12  8  1  2  1  1  6  1 12  4  1
 0  1  0  0  5  5  1  8  3  1  7 12  1 14  9 11  2  1  1  2 10 15  1  7  0  2  8  1 12  1  1 15 10  1  1  1 10  9  1  4  1  3  1 12 13 13  3  8  1  2 14  1  1  9  1 15  3  1  9  1  6  8
 0  0  1  3  3  8 15  1 11  2  2  6  7  7 13  8  1  9  6 10  9 12  0  1  4  7  1 15  9  4  9  3  1  8  8 11 12  6 12  1 11 10 13  1  1  2 10  1 15 15  6  6  5  3  4  7  1  0  5 12  1  4
 0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  8  8  8  8  8  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  8  8  0  0  0  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  0  0  8  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  8  8  8  8  8  0  8  8  8  0  8  8  8  0  0  8  8  0  8  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8  8  0

generates a code of length 62 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+524x^57+824x^58+1918x^59+1993x^60+2420x^61+1942x^62+2162x^63+1402x^64+1448x^65+796x^66+558x^67+178x^68+124x^69+22x^70+30x^71+8x^72+28x^73+4x^75+1x^76+1x^80

The gray image is a code over GF(2) with n=496, k=14 and d=228.
This code was found by Heurico 1.16 in 5.1 seconds.