The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  0  1  1  1  6  1  1 10  1  1 12  1  1  0  1  6  1  1  1 12 10 10  1  0 10 12  1  1  1  1  1  6  2  1  1  1  1  1  1  1
 0  1  3  6  5  1 12 15  1 10  9  1  0  1  3  6  5  1 12  9  1 10 15  1  0  9  1  3  1  6 15 12  1  1  1  3  1  1  1 10  6 10 10  0  1  1  5 10  6 12  2  5  0
 0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  8  8  0  8  0  0  0  8  8  8  8  0  8  8  0  8  8  8  0  0  8  0  8  8  0  8  8  8  0  0  0  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  8  8  0  0  8  0  8  0  0  8  0  8  0  8  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  0  0  8  0  0  8  8  8  0  0
 0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  0  8  8  8  0  0  0  8  0  8  8  0  8  0  8  0  8  0  0  0  0  0  8  8  8  8  0  0  8  0  0  0  0
 0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  8  8  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  8  0  8  0  0  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+26x^46+64x^47+164x^48+424x^49+527x^50+1088x^51+1085x^52+1456x^53+1079x^54+1088x^55+516x^56+424x^57+149x^58+64x^59+21x^60+8x^62+2x^64+2x^68+2x^70+1x^72+1x^78

The gray image is a code over GF(2) with n=424, k=13 and d=184.
This code was found by Heurico 1.16 in 0.709 seconds.