The generator matrix

 1  0  0  0  1  1  1  2 10  1 12  1  1  1 14 12 14  0  1  6  1  1  0  2  1 12  2  1  1  1  2 12  2  1  1 10 10  0  1  8  2  1  1  1  1  0 10 14  1  8  1  1
 0  1  0  0  0  9  5  1  1  8  1  4  7 11  0  1 10 10  2  1 10  5  1 12  1  4  1 10  5  9  6  1  1 14  9  0  2  1  8  1  4 15 12  7  8  2  1  0  5  1  2  8
 0  0  1  0  1  1  4  5  2 10  3  3 12  5  1  5  1 14  3 10 14  7  8  1 14  1  7  0 15  2  1  6 12  6  1  0  1 15  0  8  1 12 10 10  6  1 11 14  7 15  5  0
 0  0  0  1  1  4  1  1 15  9  6 10 14 11  9  5  3  1  1 10  7 11 11 15 13 10 12  4 14  0 10  9  4  2  0  1  9  1  0  4  6 11  5  0 11  3  9  1 12  3  8  4
 0  0  0  0 12  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  4 12 12 12  4 12 12 12  8  8  4  4  4  4 12 12 12  8 12  4  4 12  8  8  4 12  8  8

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

Homogenous weight enumerator: w(x)=1x^0+131x^44+988x^45+2999x^46+6400x^47+11903x^48+19994x^49+29024x^50+38192x^51+41668x^52+38648x^53+30767x^54+20596x^55+11096x^56+5572x^57+2565x^58+1000x^59+337x^60+172x^61+46x^62+20x^63+16x^64+2x^65+7x^66

The gray image is a code over GF(2) with n=416, k=18 and d=176.
This code was found by Heurico 1.16 in 479 seconds.