The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+98x^39+483x^40+1338x^41+2942x^42+4630x^43+7633x^44+9694x^45+11665x^46+10082x^47+7858x^48+4632x^49+2623x^50+1024x^51+487x^52+198x^53+79x^54+32x^55+18x^56+10x^57+3x^58+6x^59

The gray image is a code over GF(2) with n=368, k=16 and d=156.
This code was found by Heurico 1.16 in 25.5 seconds.