"mean doing" is wrong. It doesn't exist.

Using the infinitive "to do" or the gerund "doing" changes the sentence. For example, "it means doing the floor again" signifies the result of something. "I mean to do the floor" signals my intent to do the floor. There are several verbs like this where using an infinitive or gerund changes the sentence. The verb "stop" is one such. "I stopped to call home" is much different from "I stopped calling home".