An augmented metric space is a metric space equipped with a function . This type of data arises commonly in practice, e.g., a point cloud in where each point has a density function value associated to it. An augmented metric space naturally gives rise to a 2-parameter filtration . However, the resulting 2-parameter persistent homology could still be of wild representation type and may not have simple indecomposables. In this paper, motivated by the elder-rule for the zeroth homology of 1-parameter filtration, we propose a barcode-like summary, called the elder-rule-staircode, as a way to encode . Specifically, if , the elder-rule-staircode consists of number of staircase-like blocks in the plane. We show that if is interval decomposable, then the barcode of is equal to the elder-rule-staircode. Furthermore, regardless of the interval decomposability, the fibered barcode, the dimension function (a.k.a. the Hilbert function), and the graded Betti numbers of can all be efficiently computed once the elder-rule-staircode is given. Finally, we develop and implement an efficient algorithm to compute the elder-rule-staircode in time, which can be improved to if is from a fixed dimensional Euclidean space , where is the inverse Ackermann function.