Error Correcting Code

If no two strings in a code differ in fewer than three positions, the we can actually correct a single error, by finding the unique string in the code that differs from the received string in only one position.  It turns out that there is a code of 7-bit strings that corrects single errors and contains 16 strings.  Find such a code.

Hint: Reasoning it out is probably best, but if you get stuck, write a program that searches for the string.

From the example in the book - the strings would be like ASCII sequence of bits - whereby ASCII has a seven bit code and then a parity bit placed on the front for error detecting.