This is part of the main missions of the game, so it's unmissable.
https://starbounder.org/The_Erchius_Mining_FacilityAfter finding Esther at The Ark/Outpost, she'll give you a quest to fix your ship, so you'll be able to visit the galaxy map and move around to more planets. You'll soon be sent to go to The Erchius Mining Facility, you can find this by talking to the AI on your ship, and looking under the missions tab. You'll want to make sure you have made the first set of Iron armor, and have a decent weapon or two. This is a pretty simple area where you'll need to make your way downwards, where you'll fight the first boss of the game, the Erchius Horror. Make sure you explore a bit as well though, as this area will have a few of the codices you will need towards the 100 total found. You'll be able to come back to this area after completing it at any time though if you missed any of the codices.
A pretty simple boss fight, just turn on the four switches around the boss arena, which will power the laser under the boss. You'll need to repeat this three times, to defeat the boss with the laser. After that you'll be able to gather the materials to fix your ship. Return to Esther to turn in the quest, and this will unlock.