  Observations of very early multi-wavelength afterglows are critical to reveal
the properties of the radiating fireball and its environment as well as the
central engine of gamma-ray bursts (GRBs). We report our optical observations
of GRB 111228A from 95 sec to about 50 hours after the burst trigger and
investigate its properties of the prompt gamma-rays and the ambient medium
using our data and the data observed with {\em Swift} and {\em Fermi} missions.
Our joint optical and X-ray spectral fits to the afterglow data show that the
ambient medium features as low dust-to-gas ratio. Incorporating the energy
injection effect, our best fit to the afterglow lightcurves with the standard
afterglow model via the Markov Chain Monte Carlo (MCMC) technique shows that
$\epsilon_e=(6.9\pm 0.3)\times 10^{-2}$, $\epsilon_B=(7.73\pm 0.62)\times
10^{-6}$, $E_{\rm K}=(6.32\pm 0.86)\times 10^{53}\rm erg$, $n=0.100\pm 0.014$
cm$^{-3}$. The low medium density likely implies that the afterglow jet may be
in a halo or in a hot ISM. Achromatic shallow decay segment observed in the
optical and X-ray bands is well explained with the long-lasting energy
injection from the central engine, which would be a magnetar with a period of
about 1.92 ms inferred from the data. The $E_p$ of its time-integrated prompt
gamma-ray spectrum is $\sim 26$ KeV. Using the initial Lorentz factor
($\Gamma_0=476^{+225}_{-237}$) derived from our afterglow model fit, it is
found that GRB 111228A satisfies the $L_{\rm iso}-E_{\rm p,z}-\Gamma_0$
relation and bridges the typical GRBs and low luminosity GRBs in this relation.
