Write permission in home directory [closed]

Question

Root doesn't have write permissions in my home directory, and every bin or sh file I want to run, needs to be run from root. My user has access to the files, but can't run them because its not root.

How do I enable write permissions to my home directory for the root?

EDIT:

ls -lad "$HOME" 
drwxr-xr-x+ 33 userid groupname 42 Aug  4 22:59 /home/userid

EDIT2: Output from getfacl /home/userid

getfacl: Removing leading '/' from absolute path names
# file: home/userid
# owner: userid
# group: groupname
user::rwx
group::r-x
mask::rwx
other::r-x

EDIT 3: Output from df $HOME

Filesystem            1K-blocks       Used  Available Use% Mounted on
xxxxxxxx:/export/home1/userid
                     5156362272 3035249664 2121112608  59% /home/userid