Free PSN codes are available from time to time as giveaways in the Playstation Network but if you want to get them, you will have to be patient as there is no way you can predict when Sony will release them and why. No later than February 2014, Playstation gave away free psn codes to their users. Overnight, Playstation owners received $10 and a message that states: PSN codes for $10. It was a good marketing campaign and as a consequence, we might expect a new one in the following months.
Free PSN codes are otherwise hard to find on the internet, especially since there are no legit sites to give them, at least none that I know of. I know, a quick search on Google for the specific keywords will give you hundreds of websites with free codes. However, do not bother with them, they are not for real, except for the http://ihacksncodes.com/psn-code-generator/ website.
If you are packed with patience however, you may still get the next Playstation giveaway of free PSN codes and solve all your problems, at least for a short while. Or you can always pay for them and use your PS4 console at its maximum potential. It may be the simplest way to get a working code from a reliable source.