  Enhancing robustness of topological orders against perturbations is one of
the main goals in topological quantum computing. Since the kinetic of
excitations is in conflict with the robustness of topological orders, any
mechanism that reduces the mobility of excitations will be in favor of
robustness. A strategy in this direction is adding frustration to topological
systems. In this paper we consider a frustrated toric code on a kagome lattice,
and show that although increasing the strength of perturbation reduces the
topological order of the system, it cannot destroy it completely. Our
frustrated toric code is indeed a quantum loop gas model with string tension
and pressure which their competition leads to a partially topological phase
(PTP) in which the excitations are restricted to move in particular
sublattices. In this phase the ground state is a product of many copies of
fluctuating loop states corresponding to quasi one dimensional ladders. By
defining a non-local matrix order parameter and studying the behavior of ground
state global entanglement (GE), we distinguish the PTP from the standard
topological phase. The partial mobility of excitations in our system is a
reminiscent of fracton codes with restricted mobility, and therefore our
results propose an alternative way for making such a restriction in three
dimension.
