Yes, nobody does that. The SI base unit of mass is the kilogram, not the gram. (Yes, it's weird that that's the case. No, it's still not a good idea to buck the trend.)
...which brings us back to 4 kkg -- 4 kilokilograms!
Honestly we should just introduce a new name for the kilogram and make the gram a millifoo.
Millifoo has a mellifluous sound to it.
In the original version of the metric system, the base unit of mass was the grave, corresponding to the kilogram. 1/1000 of a grave was a gravet.
And from what I heard, grave sounded to much like 'duke' (in French or German), so the French Revolutionaries weren't too keen on it.
The French word for 'duke' would be 'duc' (pronounced more or less identically to the English word, for the obvious reason that the English word is borrowed from French). The German word appears to be Herzog. It's hard to see where either word might be plausibly confused with any possible pronunciation of "grave".