Starbase 414

From Memory Alpha, the free Star Trek reference.

Starbase 414 was a Federation starbase administered by Starfleet.

Around 2367 the USS Goddard resupplied at Starbase 414. (TNG: "Brothers" et al.)

The assignment of the Goddard was not mentioned on screen, but rather was seen on a Starship Mission Status chart in the observation lounge during Star Trek: The Next Generation's run.