When doing a code search it searches by power, which the roku lacks, so it would fail. Those are UEI made remote's roku codes. When testing, tune to home screen, use the cursor keys to move around the grid.
see this page: https://www.roku.com/accessories You want remote 4th on the list, the Enhanced Voice Remote, it doesn't list roku 3, but it WILL work. If you don't need headphone jack on the remote, and want to save $10.00 go for the second remote, the Roku Voice Remote. its thinner then then your roku remote. The fifth remote is listed as Roku 3, but its just like one you already have no volume, only remotes listed with Tv Power & Volume have that feature.