The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+160x^54+140x^55+567x^56+912x^57+1656x^58+2568x^59+3481x^60+4540x^61+4868x^62+4540x^63+3346x^64+2728x^65+1592x^66+816x^67+451x^68+140x^69+132x^70+67x^72+40x^74+17x^76+3x^80+3x^84

The gray image is a code over GF(2) with n=496, k=15 and d=216.
This code was found by Heurico 1.16 in 22 seconds.