What is meant by encrypting/decrypting a known plaintext/ciphertext with every possible key in meet-in-the-middle?
Your question has given to you only 20-bit key space so, you can achieve it. As mentioned earlier, even storing one full table is not an easy job and accessing $2^{56}$,too, although we know that Titan can reach $2^{62}$ around one hour, it is a supercomputer. Your task simply says that your key will be in the format in binary case as:

xxxxxxxpxxxxxxxpxxxxxx0p0000000p0000000p0000000p0000000p0000000p


so you have to iterate for x's from

0000000p0000000p0000000p0000000p0000000p0000000p0000000p0000000p


to

1111111p1111111p1111110p0000000p0000000p0000000p0000000p0000000p


and store them in a table T1 ( or hash map). (There are 64-bit over there). The p represents the parity bits.

From Wikipedia:


  Initially, 56 bits of the key are selected from the initial 64 by Permuted Choice 1 (PC-1)—the remaining eight bits are either discarded or used as parity check bits


In the next step, use the same iteration for the decryption and look for the result in T1.