If you want to preserve the syntax coloring/highlighting that appears in whatever code editor you use, I suggest that you use a screenshot application to capture the snippets from the editor as graphical files (such as *.jpg or *.png) that you can insert into Word documents. Inserting RTF text into Word, while it does preserve the syntax formatting, fails the other requirements of a single object per snippet and isolation from the rest of the document.
I'm familiar with Snagit from TechSmith, which easily scrolls text to capture multiple-screen objects. It also has tools for adding callouts, cropping and splitting images, and other useful operations. Other applications may have similar features.
If you expect to edit the captured text, you can't do that easily with a graphical image. Instead, you should make a copy of the original code file, edit it, and then take a screen shot.
For the labeling of a snippet, once it's inserted as a picture, you can use Word's built-in Insert Caption dialog to enter the label text. If necessary, the font and/or paragraph format of the style named "Caption" can be modified.