We present ALMA continuum and spectral line observations of the young Brown Dwarf \rho -Oph 102 at about 0.89 mm and 3.2 mm . We detect dust emission from the disk at these wavelengths and derive an upper limit on the radius of the dusty disk of \sim 40  AU . The derived variation of the dust opacity with frequency in the mm provides evidence for the presence of mm-sized grains in the disk outer regions . This result demonstrates that mm-grains are found even in the low density environments of Brown Dwarf disks and challenges our current understanding of dust evolution in disks . The CO map at 345 GHz clearly reveals molecular gas emission at the location of the Brown Dwarf , indicating a gas-rich disk as typically found for disks surrounding young pre-Main Sequence stars . We derive a disk mass of \sim 0.3 - 1 %  of the mass of the central Brown Dwarf , similar to the typical values found for disks around more massive young stars .