here's another way to do it directly in CATIA:
Use MEASURE INERTIA and customize it to include PRINCIPAL AXES. Measure the Inertia of the Part Body, and KEEP the measurements. You'll see the part envelope displayed around the part.
Look in the tree at the bottom of the Analysis branch - you'll find three BBL values. These are the x,y,z lengths of the Boundary Box, based on the inertia axis.