If Disk Utility can't repair the volume, it means that its directory structure is damaged to point where it can't find all catalogued files any more.
While you can now try copying all files to another disk, this may result in lots of errors, and you may also not get all files that are still theoretically recoverable.
Therefore, I recommend that you use the product Data Rescue for this recovery job. It scans the entire disk (takes a while), searching for "lost fragments" of the catalog, trying its best to recover as much as possible.
With a disk that's marked unrepairable, you should not try to keep writing to it (in fact, it should be made read-only, which is, sadly not as simple any more as it used to be long ago), because any further writes may overwrite valid data, due to the damaged catalog.
So, get a large enough second disk and start rescuing. Do not attempt to fix this volume unless you do not care for more losses.