The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+55x^52+142x^53+215x^54+584x^55+887x^56+1658x^57+3215x^58+5010x^59+7133x^60+9138x^61+9634x^62+8900x^63+7470x^64+4920x^65+3083x^66+1714x^67+757x^68+470x^69+187x^70+164x^71+73x^72+46x^73+45x^74+10x^75+7x^76+10x^77+4x^78+1x^80+1x^82+2x^83

The gray image is a code over GF(2) with n=496, k=16 and d=208.
This code was found by Heurico 1.16 in 50 seconds.