Super-Kamiokande has been searching for neutrino bursts characteristic of core-collapse supernovae continuously, in real time, since the start of operations in 1996. The present work focuses on detecting more distant supernovae whose event rate may be too small to trigger in real time, but may be identified using an offline approach. The analysis of data collected from 2008 to 2018 found no evidence of distant supernovae bursts. This establishes an upper limit of 0.29 yr− 1 on the rate of core-collapse supernovae out to 100 kpc at 90% CL For supernovae that fail to explode and collapse directly to black holes the limit reaches to 300 kpc.