Optional argument's value could not be transferred for the `*matrix` environment in l3doc

I have to write pmatrix in the l3doc class when conducting a math-related package, and I also have to use the mathtools package to typeset the small matrix. I found that after I define a token list (It's a l3tl, but I use it in l2e environment just for writing this MWE :-))

\ExplSyntaxOn\tl_set:Nn \foo { r }\ExplSyntaxOff

Then, I can use it directly like

% \usepackage{mathtools}\[  \begin{psmallmatrix*}[\foo]    1 & 2\\    3 & 4  \end{psmallmatrix*}\]

But I could not use it like the case

\[  \begin{pmatrix*}[\foo]    1 & 2\\    3 & 4  \end{pmatrix*}\]

which differs with a small prefix, returns me the following error 10 times!

Package array:  Illegal pream-token (\foo): `c' used.

But if I switch to the standard class, like article, the errors disappeared.

I've referred l3doc.dtx, and I think it's due to shortvrb, and I disabled | and ", but this does not work, and I've also tried applying \expandafter, it's also not work.The full MWE is the following

\documentclass{l3doc}\usepackage{mathtools}\begin{document}\ExplSyntaxOn\tl_set:Nn \foo { r }\ExplSyntaxOff\[  \begin{psmallmatrix*}[\foo]    1 & 2\\    3 & 4  \end{psmallmatrix*}\]\[  \begin{pmatrix*}[\foo]    1 & 2\\    3 & 4  \end{pmatrix*}\]\end{document}