Largest set of 10-digit numbers where none have Hamming Distance = 1 with any other


I’m working on a system that will require manual data entry of 10-digit numbers (Σ = 0123456789). To help prevent data errors, I want to avoid generating any two strings that have a hamming distance of 1.

For example, if I generate the string 0123456789 then I never want to generate any of these strings: {1123456789, 2123456789, 3123456789, …}

What is the largest set of unique strings in the universe of possible strings that satisfy the constraint where no two strings have a hamming distance of 1? If this set can be identified, is there any reasonable way to enumerate it?