  We study the production of the spin partner of the X(3872), which is a
D^{*}\bar D^{*} bound state with quantum numbers J^{PC}=2^{++} and named
X_2(4012) here, with the associated emission of a photon in electron--positron
collisions. The results show that the ideal energy region to observe the
X_2(4012) in e^+e^- annihilations is from 4.4~GeV to 4.5~GeV, due to the
presence of the S-wave \bar D^{*} D_1(2420) and \bar D^{*} D_2(2460)
thresholds, respectively. We also point out that it will be difficult to
observe the \gamma X(4012) at the e^+e^- center-of-mass energy around 4.26~GeV.
