Find a subsheaf of a coherent sheaf, whose quotient is torsion sheaf.

Question

Suppose $X$ is a variety, $\mathcal{F}$ is a coherent sheaf, its generic stalk has rank $r$. How to find an ideal sheaf $I$ such that a direct sum of $r$ copies of $I$ injects into $\mathcal{F}$ and $$0\to\oplus_r\mathcal{I}\to \mathcal{F}\to \mathcal{F}/\oplus_rI\to 0$$ the quotient sheaf vanishes on the generic stalk?