TextMate grammar: detecting whitespace-indented comments

Question

I've got a toy (fictional) programming language I'm playing around with called Nyx. I want to create a basic TextMate grammar for it so that I have basic syntax highlighting in VS Code.

The behaviour I want around comments is that there's only one way to start a comment; by using the '' char sequence. The key is that the comment also includes any subsequent lines that are indented more than the '' that started the comment. Here's an example:

This is not a comment

'' This IS a comment
   So is this

   And this also

This is NOT a comment

some.code(that.isNot(aComment)) '' This IS a comment
                                   And this second line is too!

back.toCode<Again>()

How can I create such a TextMate rule for Vs Code? In my repository section I have made a start (based on a few bits I've seen online of other people's grammars) with:

"comments": {
      "patterns": [
        {
          "name": "comment.line.double-apos.nyx",
          "begin": "(^[ \\t]+)?(?='')",
          "beginCaptures": {
            "1": { "name": "punctuation.whitespace.comment.leading.nyx" }
          },
          "end": "(?!\\G)"
        }
      ]
    }

but I'm unsure how to continue; I don't know of another language with comments that work this way so I don't have anything I can copy from.