E, welcome to the site. 

You should try the `predictmeans::predictmeans()` function - this will take the fitted model and produce graphs with least significant difference bars which will clearly show which groups are different from one another. The function also allows you to chose a method for correcting when conducting multiple comparisons. 

I wouldn't recommend boxplots for the above mentioned reason in the comments and they only way I have seen them used to show differences between groups is putting letters above them to show which pairs are different - this is quite confusing for the reader though.

Let me know if you have anymore questions.