The generator matrix

 1  0  0  1  1  1  2  1  1 12  1  1 14  6  6  0  1  1 14  1  1  8  1 12  2  1  8  1  1  1  1  1  4  1  1  1  1 10 14  6  4 12 12  1  1  1  4 14  0  6  1  1
 0  1  0  4  5  7  1  2  1  1  3  6  1  6  1  1 12 11  4 14  7  1 10  6  1  1  1 12 15 14  1  5  1  1 12 14  9  0  1  6  1 12  1  2 11  8  1  1  1  1  3  0
 0  0  1  7  3  2  1  1  4  3  5  6  2  1  0  5  6  4  1  7  7  2  0  1  7  2  7  5  3 10  9  0  1  7 11 14 15  1  8  1  9  1  4 13  4  1  9 10 10  5  0  0
 0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  8  8  8  8  8  0  8  0  0  0  8  8  0  0  8  0  8  0  0  0  8  8  0  0  0  0  0  0  8  8  0  8  8  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  0  8  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  0  0  8  8  8  8  0  8  8  8  8
 0  0  0  0  0  8  0  0  8  0  8  8  8  8  0  8  8  8  0  0  0  8  0  8  0  0  0  0  0  8  8  8  0  8  8  0  0  0  8  0  0  8  8  8  0  8  0  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  8  0  0  0  0  8  8  0  8  0  8  8  8  8  0  0  0  8  0  8  8  8  8  8  0  0  8  0  0  0  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+30x^44+224x^45+656x^46+1744x^47+2834x^48+4838x^49+7620x^50+9000x^51+11502x^52+9270x^53+7779x^54+4838x^55+2672x^56+1482x^57+562x^58+286x^59+106x^60+50x^61+20x^62+2x^63+5x^64+8x^65+2x^66+2x^67+2x^68+1x^70

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 28.9 seconds.