When looking for companies that may have an interest in your wares, consider working for a smaller company that is unable to hire someone full-time at the going market rate, but would be willing to bring you on part-time.
By working part-time, you are often more able to gather higher-level experience than if you sought a lower-level, permanent, full-time position. And by working with a smaller company, the experience will likely be much broader, since each person often wears many different hats.
If you do outstanding work for them, they will be happy to give you an excellent reference. Or they may surprise you by offering you full-time work in some combination of duties. It's a start—and often that is all it takes.