  We study an inertial Brownian particle moving in a symmetric periodic
substrate, driven by a zero-mean biharmonic force and correlated thermal noise.
  The Brownian motion is described in terms of a Generalized Langevin Equation
with an exponentially correlated Gaussian noise term, obeying the
fluctuation-dissipation theorem. We analyse impact of non-zero correlation time
of thermal noise on transport properties of the Brownian particle. We identify
regimes where the increase of the correlation time intensifies long-time
transport of the Brownian particle. The opposite effect is also found: longer
correlation time reduces the stationary velocity of the particle. The
correlation time induced multiple current reversal is detected. We reveal that
thermal noise of non-zero correlation time can radically enhance long-time
velocity of the Brownian particle in regimes where in the white noise limit the
velocity is extremely small. All transport properties can be tested in the
setup consisting of a resistively and capacitively shunted Josephson junction
device.
