German native here. This sentence means "I have no country and no home (country)." Heimat is always a larger area, not just one house or one city. Could be a region or a country. Also, while Land can technically be land / real estate, that's a really uncommon use for it and it took me a moment to even realize that it could mean that. Land should always be translated as "country".
US English-speaking here, but one of Duo's 'correct' solutions for this is "I do not have a country and no home". I guess it would depend on the inflection/cadence of the speaker, but that sentence does not look good to me. "I have no country and no home" sounds great, as does "I do not have a country and I don't have a home" or "I don't have a country nor a home". Mixing "don't have a" in with "no" just sounds very unnatural to me even though it doesn't appear to be breaking any rules. Am I alone in feeling this way? Maybe putting a comma after 'country' would help, because the way it's written, it sounds to me like 'I do not have no home'.
well then this is a good read for you: https://deterritorialinvestigations.files.wordpress.com/2015/03/boltanski-luc-new-spirit-capitalism.pdf