Stardate 1553.2

Heading back to Starbase 11 with the remains and personal effects of the Antares crew, as well as their research and data...

Naval ships usually have home ports, if you haven't figured it out by now, Starbase 11 is the home port for Enterprise

Supplemental: Spock reviewed the Antares log -- they knew the reactor was going critical, but didn't know about the missing baffle plate...

You got to figure they knew something was going wrong and they were desparately trying to fix it when time ran out.