What code did the Enigma break?

None, the Enigma was a cipher produced by an Enigma machine. The Enigma cipher was broken by using a machine called a Bombe that was invented by the Poles and improved on by the British and later Americans.
The enigma ws the named code.
The Poles had broken Enigma in 1932, when the German encoding machine was undergoing its trials with the German Army. However, when the Poles broke Enigma, the cipher altered only once every few months. This ment that the Polish had time to sudy the codes seqquences. When the war started, The Germans made the code change once each day, normally at midnight, This then gave the odds on cracking the code as159 million million million possible settings which could be chosen from.
The Polish informed the British in July 1939 once they needed help to break Enigma and with invasion of Poland imminent so that any work could be contiinued.

The Code Section and listening posts were at Bletchly Park (in the UK). As more and more people arrived to join the codebreaking operations, the various sections began to move into large pre-fabricated wooden huts set up on the lawns of the Park. For security reasons, the various sections were known only by their hut numbers.

The first operational break into Enigma came around the 23 January 1940, when the team working under Dilly Knox, with the mathematicians John Jeffreys, Peter Twinn and Alan Turing, unravelled the German Army administrative key that became known at Bletchley Park as 'The Green'. EBecause of this success, the Codebreakers managed to crack the 'Red' key used by the Luftwaffe liaison officers co-ordinating air support for army units. Gordon Welchman, soon to become head of the Army and Air Force section, devised a system whereby his Codebreakers were supported by other staff based in a neighbouring hut, who turned the deciphered messages into intelligence reports.