The generator matrix

 1  0  1  1  1  6  1  1 12 10  1  1  1  1  1  8  1 14  4  1  1  1  2  1  1  1  1  1  8  6  1  1  1  1 10  1  1  1 14  1  8  0  1  1  1  1  1  0  1  4  0  1  4  1  1  2  1  0  1  1  1  1
 0  1 11  6 13  1 12  3  1  1 10  5 15  9  8  1 14  1  1 11  2  4  1 13  7  1  0  2  1  1  1 10  3  8  1  2  6  5  1  5  1  1  3  1  6 12  0  1  9  1  1  9  1  3 13  1 13  1 10  1  0  0
 0  0 12  0  4  0  0  8  8  0  8  0  8  8  4  4  4 12  4  4 12  4  4  4  4  4  8  4 12  0  4  0  8  4  0 12  0  8 12  8 12  8  8 12  8  0  0  0  0  4 12  4  4  8  4 12  0  0  8  0  8  0
 0  0  0  8  0  0  0  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0  8  0  8  0  8  8  0  8  0  8  0  8  0  8  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  8  8  0  8  8  8  8  0  0  8  0  0  8  8  8  0
 0  0  0  0  0  8  0  0  8  0  0  8  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0  0  0  0  8  8  0  0  8  0  0  0  8  8  8  8  8  0  8  0  8  8  0  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  0  8  0  8  0  0  8  8  0  0  8  0  0  8  8  8  0  0  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  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+46x^54+36x^55+354x^56+268x^57+1084x^58+836x^59+2531x^60+1420x^61+3314x^62+1420x^63+2508x^64+836x^65+1044x^66+268x^67+276x^68+36x^69+54x^70+16x^72+16x^74+7x^76+10x^78+1x^80+2x^84

The gray image is a code over GF(2) with n=496, k=14 and d=216.
This code was found by Heurico 1.16 in 3.48 seconds.