    \documentclass{article}

    \usepackage{agda}

    \usepackage{amsmath}
    \usepackage{newunicodechar}
    \newunicodechar{₁}{\ensuremath{{}_{\text{1}}}}

    \pagestyle{empty}

    \begin{document}

    \noindent Control:
    \begin{code}
      _ : Set₁
      _ = Set
    \end{code}

    \noindent No extra indentation (alignment):
    \begin{code}[hide]
      _ : Set₁
      _ =
    \end{code}
    \begin{code}
        Set
    \end{code}

    \noindent No extra indentation (indentation):
    \begin{code}[hide]
      _ : Set₁
      _ =
    \end{code}
    \begin{code}
         Set
    \end{code}

    \noindent No extra indentation (alignment):
    \begin{code}[hide]
      postulate
        _ :
    \end{code}
    \begin{code}
          Set
    \end{code}

    \noindent No extra indentation (indentation):
    \begin{code}[hide]
      postulate
        _ :
    \end{code}
    \begin{code}
           Set
    \end{code}

    \noindent No extra indentation (alignment, \texttt{AgdaMultiCode}):
    \begin{AgdaMultiCode}
    \begin{code}[hide]
      _ : Set₁
      _ =
    \end{code}
    \begin{code}
        Set
    \end{code}
    \begin{code}[hide]
      _ : Set₁
      _ =
    \end{code}
    \begin{code}
        Set
    \end{code}
    \end{AgdaMultiCode}

    \noindent Extra indentation (indentation, \texttt{AgdaMultiCode}):
    \begin{AgdaMultiCode}
    \begin{code}[hide]
      _ : Set₁
      _ =
    \end{code}
    \begin{code}
         Set
    \end{code}
    \begin{code}[hide]
      _ : Set₁
      _ =
    \end{code}
    \begin{code}
         Set
    \end{code}
    \end{AgdaMultiCode}

    \noindent No extra indentation (alignment, \texttt{AgdaMultiCode}):
    \begin{AgdaMultiCode}
    \begin{code}[hide]
      postulate
        _ :
    \end{code}
    \begin{code}
          Set
    \end{code}
    \begin{code}[hide]
      postulate
        _ :
    \end{code}
    \begin{code}
          Set
    \end{code}
    \end{AgdaMultiCode}

    \noindent Extra indentation (indentation, \texttt{AgdaMultiCode}):
    \begin{AgdaMultiCode}
    \begin{code}[hide]
      postulate
        _ :
    \end{code}
    \begin{code}
           Set
    \end{code}
    \begin{code}[hide]
      postulate
        _ :
    \end{code}
    \begin{code}
           Set
    \end{code}
    \end{AgdaMultiCode}

    \noindent Extra indentation (indentation, \texttt{AgdaMultiCode}):
    \begin{AgdaMultiCode}
    \begin{code}[hide]
      postulate
        Aaa :
    \end{code}
    \begin{code}
          Set
    \end{code}
    \begin{code}[hide]
      postulate
        Bbb :
    \end{code}
    \begin{code}
          Set
    \end{code}
    \end{AgdaMultiCode}

    \end{document}