This paper addresses the problem of distributed state estimation for linear systems with process and measurement noise, in the case of limited communication data rate, where the data exchanged between agents is quantized. We propose a linear distributed Luenberger observer and we derive a set of conditions on the design parameters of the quantizer to guarantee ultimate boundedness of the estimation error. The latter is shown to depend on the L-2 norm of the disturbance signals and on the number of bits. A numerical example illustrates the performance of the proposed algorithm.