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  1  2  1  1  1  1  2  1  1  1  1  4  1  1  0  1  2  1  4  1  1  4  1  1  4  1
 0 12  0 12  0 12  0  4  8 12  0 12 12  0  8  4  8 12  4  0  0  4 12  8  8 12  4 12  0  0  8  0 12  0  8  8  8 12  0  0  4  0 12  0  8 12  4  0  4  4  8  8
 0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  8  0  8  0  0  0  0  0  8  8  8  0  8  8  0  8  0  0  0  0  8  8  0  0  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  8  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  0  8  8  0  8  8  0  8  8  8  0  0  8  8  0  8  8  8  8  0  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  8  8  0  0  0  0  8  8  8  0  8  0  8  8  8  8  8  0  8  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8
 0  0  0  0  0  8  0  8  0  8  8  0  0  8  8  0  8  0  0  8  0  0  8  8  0  0  8  8  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  0  0  8  8  8  8  8  0
 0  0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  0  8  8  8  8  8  8  8  8  0  8  0  0  0  8  8  0  0  0  8  0  0  8  8  0  8  0  8  8  8  0  0  0  0  8  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+27x^46+98x^47+62x^48+40x^49+102x^50+654x^51+142x^52+592x^53+110x^54+98x^55+42x^56+8x^57+10x^58+42x^59+2x^60+5x^62+4x^63+5x^64+2x^70+1x^72+1x^88

The gray image is a code over GF(2) with n=416, k=11 and d=184.
This code was found by Heurico 1.16 in 0.181 seconds.