How to recognise the number of errors that can be detected and corrected of a large set of codewords (k) each having a specified number of bits (n)?
There are $2^{10}$ binary strings of length $10$. We can partition them into pairs $x_1\ldots x_90,x_1\ldots x_91$. Since your code contains more than $2^9$ codewords, it will contain at least one such pair. Hence the minimum distance of your code is only $1$.