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  8  2  1 12  0  2  1  2  2 12  2  1  1  1  1  2  1  8  1  1  1  1  2  1  1  1  2  2  1
 0  2  0  2  0  0  6  6  4 14  2  4 12 14  2 12 12  2 10  4 10  8  6  4  4  8  8  2 10  2  2 10  2  2 12 12  6  4 14 10  2  0 10  0  4  8 10 10  2  0 10  0
 0  0  2  2 12  6  6  0  4  4 14  2  0  2 12  6 10 10 12 12  6 14  6  2  2 12  2  0  6  0  4 14 14  4 14  0 12 12  4 10 12  2  0 12  8 14 14 12  2 10  0  8
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  0  0  8  0  8  8  8  0  8  8  8  0  0  8  0  8  8  0  0  0  8  8  0  0  0  0  8  0  0  0  0
 0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  0  8  8  8  8  0  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  8  8
 0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  0  0  8  8  0  8  0  0  8  0  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  8  0  8  8  8  8  0  0  8  0  0  8  8  0  0  0  8  8  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  8  8  0  8  8  0  0  0  8  0  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  8  0  0  0  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+196x^44+280x^45+554x^46+940x^47+1350x^48+2516x^49+2936x^50+5404x^51+4301x^52+5556x^53+3016x^54+2628x^55+1256x^56+828x^57+484x^58+244x^59+151x^60+36x^61+46x^62+33x^64+4x^66+7x^68+1x^76

The gray image is a code over GF(2) with n=416, k=15 and d=176.
This code was found by Heurico 1.16 in 19 seconds.