The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+122x^42+644x^43+1616x^44+3156x^45+4911x^46+7448x^47+9460x^48+10852x^49+9520x^50+7988x^51+4530x^52+2736x^53+1507x^54+624x^55+255x^56+84x^57+64x^58+8x^60+4x^61+4x^62+2x^64

The gray image is a code over GF(2) with n=392, k=16 and d=168.
This code was found by Heurico 1.16 in 27.1 seconds.