Hey @brettzg,
first of all, way to go with graduating with honors. 
Second, if you want to pursue a job as a developer, you have to understand that a developer is a pretty general term. You are casting a very wide net and you need to ask yourself what type of coding job would interest you.
It can be a Backend developer, mobile developer, low-level and so on and so forth.
Once you figure out which field interests you, you can then go ahead and take the necessary steps to achieve that dream.
For most fresh graduates, places that will interview you are not going to be looking for professional experience (since you have none), but are going to want to see projects you have made and what your train of thought is.
Start by having active Github and CodePen accounts which will showcase your work.
This might be a side note, but it may be of assistance. I wrote an article about going through the motions of getting a developer job. Feel free to give it a read.