I didn't hear these two terms double errors or quadruple errors, but the minimum hamming distance of these 4 given codewords is 5, because EXOR any two pairs, and then count number of 1's in the result and then consider minimum number of 1's among all results.
Here it's 5, hence it gives a gaurantee to detect upto 4 bit errors, though it may/may not detect an error of more than 4 bits.
this is called minimum hamming distance.
It can't give a gaurantee to detect upto 5 bits error, because change into 5 bits can become another valid codeword which can't be caught. After change into 5 bits, there is a possibility that it may turn into a valid codeword.
For example if codeword is sent as 1111100000, last 5 bits are modified due to noisy channel and it becomes 11111111, now see, this is a valid codeword matching with one of the codewords.
