In this article, we obtain sucient conditions to obtain finite time blowup in a system of two coupled nonlinear Schrödinger (NLS) equations in the critical case. This system mainly considered here in dimension 2, couples one equation including gain and the other one including losses, constituting a generalization of the model of pulse propagation in birefringent optical fibers. In the spirit of the seminal work of Glassey, the proofs used the virial technique arguments.