  In this paper, we introduce a new definitions of the Gray weight and the Gray
map for linear codes over $\mathbb{Z}_9+u\mathbb{Z}_9$ with $u^2=u$. Some
results on self-dual codes over this ring are investigated. Further, the
structural properties of quadratic residue codes are also considered. Two
self-dual codes with parameters $[22,11,5]$ and $[24,12,9]$ over $\mathbb{Z}_9$
are obtained.
