Is the any QR code with built-in hash of the information? For example, the text is something like 

"Hello world!"

And after that text should be new line with hash (sha256): 

9e77bdb7b7b67bee57fe10946ac0275e38585c688ace439d96d82ebf71c26496


So, now it is not possible to modify QR code (recoloring some squares) without loosing it.

Is something like this implemented for QR coding outside, where it is possible to modify the code?
There are encrypted QR codes from DENSO ADC.  I know that these can be encrypted or just signed; however, DENSO ADC has never been forthcoming with how they work.  They seem to work by putting data after the "data section" of the QR code that would otherwise be ignored.  If you were going to have something similar, I would take that approach.