144 hours and North Korea

North Korea is treated in the same way as any other country. So, anybody traveling there has the same rights, including 144 hours visa free transit. Anyway, you will have to obtain a single entry visa since you will be returning from North Korea to Beijing by train. The only eligible train to and from Beijing when we talk about 144 hours visa free transit is a conventional one from Beijing West railway station to Hong Kong. All other international trains, including the one to/from North Korea require a visa. Having a visa would allow you to travel even between Beijing and Hong Kong using a high speed train instead of a conventional one, but I assume that you already have a plane ticket for that portion of your itinerary.

I don't know when do you plan to depart for your journey, but I suggest you to start issuing your visa as soon as possible. In your case it is enough to have just a single entry visa because you can rely for 144 hours visa free transit during your first arrival in Beijing, but you are supposed to have all the necessary documentation with you, especially the part where it will be visible that you will be flying to North Korea by plane. Please, you should do this impeccably and your agency that will guide you during your stay in North Korea should provide you with that documentation. Upon landing in Beijing, you will apply for 144 hours visa free transit and will ask the official at the desk to leave your single entry visa unused and he/she will do that. So, start completing your documentation because this detail with the train has ruined your intention to travel entirely visa free.