The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+122x^41+619x^42+1770x^43+3084x^44+5148x^45+6765x^46+10320x^47+9634x^48+10424x^49+7250x^50+5426x^51+2686x^52+1304x^53+557x^54+252x^55+109x^56+38x^57+9x^58+8x^59+4x^60+4x^61+2x^64

The gray image is a code over GF(2) with n=384, k=16 and d=164.
This code was found by Heurico 1.16 in 26.3 seconds.