Well, Cytoscape is certainly powerful enough, and provides the necessary tools to create a network manually, but I would probably recommend you start by creating a spreadsheet with your data. Most people find interacting with a spreadsheet an easier on-ramp. In your case, you might have something like:
code1 code2 interaction
and then a separate spreadsheet of all of your codes:
code description "concept group", etc.
It's very straightforward to import these into cytoscape for visualization and analysis.
-- scooter