  We report on XMM-Newton X-ray observations that reveal CTCV J2056-3014 to be
an unusual accretion-powered, intermediate polar (IP) system. It is a member of
the class of X-ray-faint IPs whose space density remains unconstrained but
potentially very high, with L$_{x,0.3-12 keV}$ of 1.8$\times$10$^{31}$ erg
s$^{-1}$. We discovered a coherent 29.6s pulsation in X-rays that was also
revealed in our reanalysis of published optical data, showing that the system
harbors the fastest-spinning, securely known white dwarf (WD) so far. There is
no substantial X-ray absorption in the system. Accretion occurs at a modest
rate ($\sim$ 6$\times$10$^{-12}$ M$_{\odot}$ yr$^{-1}$) in a tall shock above
the WD, while the star seems to be spinning in equilibrium and to have low
magnetic fields. Further studies of CTCV J2056-3014 potentially have broad
implications on the origin of magnetic fields in WDs, on the population and
evolution of magnetic cataclysmic variables, and also on the physics of matter
around rapidly rotating magnetic WDs.
