  In this letter we report on the electrical transport properties of
Bi$_4$Te$_3$ in a Josephson junction geometry using superconducting Al
electrodes with a Ti interdiffusion barrier. Bi$_4$Te$_3$ is proposed to be a
dual topological insulator, for which due to time-reversal and mirror symmetry
both a strong topological insulator phase as well as a crystalline topological
phase co-exist. The formation of a supercurrent through the Bi$_4$Te$_3$ layer
is explained by a two-step process. First, due to the close proximity of the
Al/Ti electrodes a superconducting gap is induced within the Bi$_4$Te$_3$ layer
right below the electrodes. The size of this gap is determined by analysing
multiple Andreev reflections (MARs) identified within the devices differential
resistance at low voltage biases. Second, based on the Andreev reflection and
reverse Andreev reflection processes a supercurrent establishes in the weak
link region in between these two proximity coupled regions. Analyses of the
temperature dependency of both the critical current as well as MARs indicate
mostly ballistic supercurrent contributions in between the proximitized
Bi$_4$Te$_3$ regions even though the material is characterized by a
semi-metallic bulk phase. The presence of these ballistic modes gives
indications on the topological nature of Bi$_4$Te$_3$.
