Ubuntu :: Copy Files/folders With GREP?

I'm attempting to find a particular word wherever it appears within a massive directory listing of teeny tiny text files -- and then copy all files containing this word into a "staging" directory.

Whenever I use the command below (on a test folder of smaller scale), it never carries the directory structure but attempts to copy all files within the "output" folder.

Code:
cp `grep -ir 'word' *` output

how to copy all these text files and have them retain some sort of directory structure?