As mentioned in my email, I was able to reduce the size of /skole/jener/home0. I therefore logged in als root and unmounted /skole/jener/home0.
This is usually done in two steps: first you resize (shrink) the filesystem, then you resize (shrink) the LVM partition.
The first step should look like this:
umount /dev/vg_system/home
e2fsck -f /dev/vg_system/home
resize2fs /dev/vg_system/home 90G # assuming it is 100G
For the second step you use the lvresize or lvreduce, as explained by Petter.
Dashamir