The states of matter are actually not really specific states but rather general categories of the state of a material, e. g. there are different states of ice that have a phase transition between them depending on temperature and pressure, but as they all have a essentially crystalline structure they are all considered solid.
In fact plasma is not one of these states as it is actually a different chemical state which is reached through a chemical reaction instead of a phase transition which would be necessary for a state of matter.
Antimatter should for most aspects be essentially identical to normal matter (wether there are any functional differences is subject of a lot of research) except that electrical and a few other charges are swapped. Therefore Antimatter should be able to achieve identical states as normal matter if you have atoms of equivalent cores (Anti-Hydrogen and Anti-Oxygen to form Anti-H20, etc.)
For practical purposes we are essentially only able to get very low Z (in the very upper part of the periodic system) Antimatter particles that occur primarily in gaseous form. Additionally the antimatter is usually kept in plasma form as the exposed charges of this state allow for electromagnetic containment without the antimatter coming into contact with normal matter and annealing.
So in the end: The antimatter we have is usually in a plasma state, but that is mostly for ease of handling.
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