We strongly urge you and recommend you create your own addon folder.
Placing content in 'our' addons folder will work, but, if you ever have to update just your code, or remove your code, or remove someone elses code you followed the instructions for placing thier code in our addon folder, you could end up damaging files from our addon.
To make your own addon, you'd need the following (at least for this code)
Remove addons/ulx/lua/ulx/modules/cl/motdmenu.lua
Copy your code to /addons/YOUR_addon_NAME_custom_motd_whatever/lua/ulx/modules/cl/motdmenu.
Create your own /addons/YOUR_addon_NAME_custom_motd_whatever/addon.txt (search gmod wiki or google to find out how, or base off another addon (but I'd still recommend wiki, some people just make stuff up))
Now, when ULX starts up, it will use your code.
When you update ULX, it won't overwrite your motdmenu.lua, it will just replace the missing one, and you can go remove it again.