Z3 gauge theory mimics certain properties of QCD and might even have a quantitative link when the Z3 physical degrees of freedom are identified with the core of the so-called centre vortices of QCD. In particular, the Z3 theory confines static triality charges. In this talk, I will consider Z3 gauge theory with Z3 dynamical matter. A finite chemical potential is introduced to study this theory at finite densities. Objective will be to study the deconfinement transition in the cold but dense matter region. By integrating out the gauge and matter fields, the theory can be formulated in terms of gauge invariant non-local degrees of freedom free of a sign-problem. Observables of the original theory appear as ratio of partition functions, which are evaluated by the snake algorithm. First numerical results are presented.