The ordered hexagonal perovskite Ba2CuTeO6 hosts weakly coupled S=12 spin ladders produced by an orbital ordering of Cu2+. The magnetic susceptibility $\chi$(T) of Ba2CuTeO6 is well described by that expected for isolated spin ladders with exchange coupling of J≈86K but shows a deviation from the expected thermally activated behavior at low temperatures below T∗≈25K. An anomaly in $\chi$(T), indicative of magnetic ordering, is observed at Tmag=16K. No clear signature of long-range ordering, however, is captured so far in NMR 1/T1, specific heat or neutron diffraction measurements at and below Tmag. The marginal magnetic transition, indicative of strong quantum fluctuations, is evidence that Ba2CuTeO6 is in very close proximity to a quantum critical point between magnetically ordered and spin-gapped phases controlled by interladder couplings.