Certainly you can see galaxies in your 4" refractor. See this list that Glen C has compiled.
https://www.iceinspace.com.au/63-268-0-0-1-0.html (if link does not work it is in the "projects and articles section).
Your 4' should pick up the majority of those galaxies under magnitude 10.
The difficulty will be locating them. If you have goto - fine. Otherwise you need good charts and a quality finderscope.