Embed iframe code of a Coda form to a html email sent by Gmail pack

I am researching for a way how to embed the iframe code of a Coda form into the email body and send it with Gmail pack. I am trying to use the HTML Email builder pack but somehow when I insert the iframe code, it just simply doesn’t show in the email.

Does anyone know a way how to make this happen? I want that the form shows within the email body and people can fill in the form directly in their email.

Here is the doc:

And the result:

I’m afraid iframes generally aren’t supported by email providers

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And I guess there is no other way to embed a Coda form into an email body?

I am imagining something what is possible with google forms.