The code, hand-written on a small sheet of paper headed "Pigeon Service", was found in a small red canister attached to the bird's skeleton up a chimney at a house in Bletchingley, Surrey.
Experts from UK intelligence agency GCHQ have said the message, which has 27 five-letter code groups, is impossible to crack without its codebook.
They were also left stumped by missing details, such as the date of the message and the identities of the sender, "Sjt W Stot", and the recipient, "X02".
A spokesman said: "We have had about 50 people getting in touch since our request for help was published yesterday, mainly by email but also some phone calls. They have been of varying ages, from school kids to people who were alive in the war. There have been men and women, and not just from the UK - from Holland and the USA too.
"They're approaching it from different angles, but no one has come through with a solution, saying this is what it definitely means, so the quest continues. It's still early days."
Historians believe the bird may have been dispatched from Nazi-occupied France on June 6 1944, during the D-Day invasions. Because of Churchill's radio blackout, homing pigeons were taken on the mission and released by allied forces to inform military chiefs in England how it was going.
Unlike other carrier pigeon messages, though, the one found by David Martin as he ripped out a fireplace while renovating his home is written entirely in code.
World War Two experts suspect the bird was destined for the top secret Bletchley Park, which is just 80 miles from Mr Martin's home. During the war, codebreakers worked there round the clock in top secret - deciphering Nazi codes including Enigma.
Military pigeons were dropped behind enemy lines from bombers, whereupon resistance fighters picked them up, before releasing them homeward bound with top secret messages. It is thought the destination X02 may have been Bomber Command.