The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+169x^44+320x^45+797x^46+1840x^47+2835x^48+5548x^49+6716x^50+9584x^51+9754x^52+9836x^53+6880x^54+5680x^55+2549x^56+1668x^57+714x^58+304x^59+211x^60+36x^61+59x^62+30x^64+2x^66+2x^68+1x^72

The gray image is a code over GF(2) with n=416, k=16 and d=176.
This code was found by Heurico 1.16 in 37.7 seconds.