One of the promising fields for active-stereo sensors is medical applications such as 3D endoscope systems. For such systems, robust correspondence estimation between the detected patterns and the projected pattern is the most crucial. In this paper, we propose an auto-calibrating 3D endoscopic system using a 2D grid-graph pattern, where codes are embedded into each grid point. Since the pattern is a grid graph, we use a graph convolutional network (GCN) to calculate node-wise embedding accumulating code information of nearby grid points in the graph. The correspondence estimation using the GCN-calculated feature embedding is shown to be stable, even without using epipolar constraints. Using the correspondence estimation, we show that the auto-calibrating 3D measurement system can be realized. In the experiment, we confirmed that the proposed system achieved high accuracy and robust estimation comparing to the previous methods.