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

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

Homogenous weight enumerator: w(x)=1x^0+246x^44+120x^45+829x^46+552x^47+1884x^48+2452x^49+3087x^50+5024x^51+4306x^52+5156x^53+3211x^54+2480x^55+1785x^56+444x^57+722x^58+128x^59+206x^60+20x^61+79x^62+8x^63+17x^64+7x^66+2x^68+1x^70+1x^72

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 15.2 seconds.