  Using $5.8 \times 10^7 J/\psi$ events collected in the BESII detector, the
radiative decay $J/\psi \to \gamma \phi \phi \to \gamma K^+ K^- K^0_S K^0_L$ is
studied. The $\phi\phi$ invariant mass distribution exhibits a near-threshold
enhancement that peaks around 2.24 GeV/$c^{2}$.
  A partial wave analysis shows that the structure is dominated by a $0^{-+}$
state ($\eta(2225)$) with a mass of $2.24^{+0.03}_{-0.02}{}^{+0.03}_{-0.02}$
GeV/$c^{2}$ and a width of $0.19 \pm 0.03^{+0.06}_{-0.04}$ GeV/$c^{2}$. The
product branching fraction is: $Br(J/\psi \to \gamma \eta(2225))\cdot
Br(\eta(2225)\to \phi\phi)
  = (4.4 \pm 0.4 \pm 0.8)\times 10^{-4}$.
