The Verdict: Not eligible
There is no Japanese citizenship this far back. Look at our Diaspora & Religious Return route for Japan, which has a narrow, capped residence route for fourth-generation descendants aged 18 to 35.
Japanese nationality passes from a parent only, with no provision reaching further.
Fourth-generation descendants have a separate status capped at 4,000 people a year. It needs Japanese at JLPT N5 for ages 18 to 30, or N3 for ages 31 to 35, and a supporter in Japan for the first three years. It runs to five years, after which stronger Japanese can lead to Long-Term Resident status.
Count the generations again from the ancestor born in Japan. If your grandparent was born as the child of a Japanese national, you are third generation, and the ordinary Long-Term Resident route opens with no age limit or language test.