  We study the Kitaev-Heisenberg-$\Gamma$ model with antiferromagnetic Kitaev
exchanges in the strong anisotropic (toric code) limit to understand the phases
and the intervening phase transitions between the gapped $Z_2$ quantum spin
liquid and the spin-ordered (in the Heisenberg limit) as well as paramagnetic
phases (in the pseudo-dipolar, $\Gamma$, limit). We find that the paramagnetic
phase obtained in the large $\Gamma$ limit has no topological entanglement
entropy and is proximate to a gapless critical point of a system described by
an equal superposition of differently oriented stacked one-dimensional
$Z_2\times Z_2$ symmetry protected topological phases. Using a combination of
exact diagonalization calculations and field-theoretic analysis we map out the
phases and phase transitions to reveal the complete phase diagram as a function
of the Heisenberg, the Kitaev, and the pseudo-dipolar interactions. Our work
shows a rich plethora of unconventional phases and phase transitions and
provides a comprehensive understanding of the physics of anisotropic
Kitaev-Heisenberg-$\Gamma$ systems along with our recent paper [Phys. Rev. B
102, 235124 (2020)] where the ferromagnetic Kitaev exchange was studied.
