The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+200x^41+805x^42+1536x^43+2170x^44+2222x^45+2810x^46+2298x^47+1985x^48+1198x^49+642x^50+284x^51+126x^52+58x^53+30x^54+10x^55+6x^56+2x^57+1x^58

The gray image is a code over GF(2) with n=368, k=14 and d=164.
This code was found by Heurico 1.16 in 1.65 seconds.