  The interplay of interactions and disorder in low-dimensional superconductors
supports the formation of multiple quantum phases, as possible instabilities of
the Superconductor-Insulator Transition (SIT) at a singular quantum critical
point. We explore a one-dimensional model which exhibits such variety of phases
in the strongly quantum fluctuations regime. Specifically, we study the effect
of weak disorder on a two-leg Josephson ladder with comparable Josephson and
charging energies ($E_J$~$E_C$). An additional key feature of our model is the
requirement of perfect $\mathbb{Z}_2$-symmetry, respected by all parameters
including the disorder. Using a perturbative renormalization-group (RG)
analysis, we derive the phase diagram and identify at least one intermediate
phase between a full-fledged superconductor and a disorder-dominated insulator.
Most prominently, for repulsive interactions on the rungs we identify two
distinct mixed phases: in both of them the longitudinal charge mode is a
gapless superconductor, however one phase exhibits a dipolar charge density
order on the rungs, while the other is disordered. This latter phase is
characterized by coexisting superconducting (phase-locked) and charge-ordered
rungs, and encompasses the potential of evolving into a Griffith's phase
characteristic of the random-field Ising model in the strong disorder limit.
