/usr/lib/libqwt-qt4.so is in libqwt5-qt4-dev 5.2.2-1ubuntu2.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/libqwt-qt4.so.5.2.2
/usr/lib/libqwt-qt4.so.5.2.2