The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+220x^46+580x^47+1952x^48+3092x^49+5296x^50+7216x^51+9404x^52+10040x^53+9522x^54+7204x^55+5511x^56+2980x^57+1470x^58+552x^59+315x^60+80x^61+58x^62+28x^64+10x^66+5x^68

The gray image is a code over GF(2) with n=424, k=16 and d=184.
This code was found by Heurico 1.16 in 31.2 seconds.