Oh I'm sorry I see what you mean now, the single line textbox where you enter the actual regular expression.
I would think you could make a lexer fairly easily for that where text like "(", ")", "[", "]", "+", "\w", "/g", etc. all have distinct tokens with appropriate highlighting styles for those tokens.
The tricky thing is if you want to support the background styles like they do. Since there they seem to be nesting the opacity of the background based on how many levels deep of "("..")" you go in, etc. You might be able to do that if you make a lexical state with a lexical scope that starts with "(" and ends with ")". Then duplicate all the known patterns from the default state within that and make sure those tokens have their own distinct highlighting styles with the greenish background color in addition to their normal foreground color.
I'm sorry but we don't support ANTLR4 for lexing. You can call any parser via a custom IParser language service though, so you could run your ANTLR-based parser to do parsing and error reporting. Then translate those results back to objects SyntaxEditor can use.