The solution posted by Christian may certainly help. But you may not have enough hard drive space available.
First, I am not aware of any published recommendations about the size of a catalog. My catalog is slightly larger than yours. A backup using the Adobe tool backs up not only the catalog itself (which is relatively small - about 12GB in my case), but also all of the media files. My photos take up just over 1TB and my ~10k video files also take up over 1 TB of storage.
While the size of your files may differ (and, over time, image sizes have increased), if you have anywhere near the same storage requirements as my catalog, you clearly would not have enough space for the backup.