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

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

Homogenous weight enumerator: w(x)=1x^0+69x^52+270x^53+489x^54+832x^55+1332x^56+2258x^57+3231x^58+4572x^59+6744x^60+8322x^61+9059x^62+8504x^63+6821x^64+5022x^65+3252x^66+1974x^67+1153x^68+668x^69+410x^70+222x^71+154x^72+88x^73+36x^74+22x^75+14x^76+12x^77+2x^78+2x^79+1x^82

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 71.1 seconds.