  The current trend concerning dense matter physics at sufficiently high
densities and low temperatures is expected to behave as a degenerate Fermi gas
of quarks forming Cooper pairs, namely a color superconductor, in the core of
compact objects. In this context, we study the anisotropy of quark stars (QSs)
assuming the internal composition to be comprised of homogeneous, charge
neutral 3-flavor interacting quark matter with $\mathcal{O}(m_s^4)$
corrections. Using the equation of state (EoS) with the
Tolmann-Oppenheimer-Volkoff (TOV) structure equations, we perform numerical
calculation for quark stars and determine the maximum mass-radius relation in
the context of $4D$ Einstein-Gauss-Bonnet (EGB) gravity. In particular, we
consider the effects of Gauss-Bonnet (GB) coupling constant on the diagrams
related to mass-radius $(M-R)$ relation and the mass-central mass density
$(M-\rho_c)$ relation of QSs. We pay particular attention to the influence of
the anisotropy in the equilibrium and stability of strange stars. We also study
the other properties of QSs related to compactness and binding energy.
Interestingly, our result provides circumstantial evidence in favor of
super-massive pulsars in $4D$ EGB gravity.
