/usr/lib/gcc/x86_64-linux-gnu/4.8/libquadmath.so is in libgcc-4.8-dev 4.8.2-19ubuntu1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/gcc/x86_64-linux-gnu/4.8/../../../x86_64-linux-gnu/libquadmath.so.0