This is not a standard assigned ZIP code in the immediate New Canaan area; most surrounding codes include 06850 (Norwalk) or 06903 (Stamford).
It is a popular commuter town for New York City. The Metro-North Railroad New Canaan Branch provides a direct link to Grand Central Terminal in roughly 65 minutes. 068480 zip
If "068480" was a typo for a four-digit extension or a different five-digit code: This is not a standard assigned ZIP code