Yes, you can receive your verification code by text.  Please make sure you have a current phone number listed in your Turbo Tax account. Here's how:

• Select Intuit Account in the left-hand menu.
• Under Account Settings in the SECURITY tab, enter or edit your phone number.

Please review the following Turbo Tax FAQ for more information:

https://ttlc.intuit.com/replies/4690299

Can you send me my code in a text please

We can't do that here. 

Try this:

You can update your email address.

1. Select Not your current email address?
2. Select account settings.
3. On the Intuit Account screen, update your email address under Sign In Security.
4. Return to the File section and select Start next to Step 3.

Your new email address will be listed on the verification code page and you’ll receive another verification code at that address.

OR THIS:

If you no longer have access to the email address for your TurboTax account, you can't receive an emailed verification code to authenticate your access.

The next best option is to have the verification code texted to your mobile phone. If texting isn't available, you'll need to confirm your account in a different way.

In confirm my account in a different way, you'll start by entering some info from last year's return. Be sure to use the name of the primary or first taxpayer and address information on last year's return you filed with TurboTax. There will be a couple of other questions you should know the answers to. If none of the answers shown is correct, select None of the above.

When you see the Welcome Back! screen, update your email and mobile phone contact information.