We study a transition to a glassy phase of neutral atoms trapped in optical lattice, where the system is realized as the array of individual Bose--Einstein condensates of N elongated vertical and horizontal $N$ rods in a wood-pile form coupled via the random Josephson tunneling. In this geometry every horizontal (vertical) rod of a condensate is linked to its vertical (horizontal) counterpart, so that the number of nearest neighbors "z" of a given rod in this system is z=N, implying that the system is fully connected. This together with randomness forms a prerequisite of the Sherrington-Kirkpatrick model for infinite N widely employed in the theory of spin glasses. For this arrangement we solve a model Hamiltonian of the Josephson array in the thermodynamic limit and calculate the critical temperature for the glassy phase-locking transition, caused by the Josephson tunneling of bosons in random environment.