Hi. That's so annoying, isn't it?
I use a VOIP service Callcentric.com. In some ways it is similar to Google's phone service, but, with only one exception, I've been able to use it for codes sent by banks, etc. They have a basic service, where you can forward the number they give you to any other number if you need to. They also offer a text service that is only working in the USA at present, but you can set it up to forward the message to your email account, get the code, and go from there.
It might be worth a try to see if it'd suit your needs. It's certainly cheap enough. I pay, I believe, a dollar a month for text access and ten cents per text.
https://www.callcentric.com/products/Good luck!
EDIT - Forgot to mention: you can use CC on a desktop/laptop, on a smartphone, or hook it up to an adapter that hooks to the internet and use it with an old-fashioned telephone handset.