Assuming that this imprinted code actually exists, exactly how would "The Government" (cue dramatic music) track someone down?
Simple, they decode the pattern on the print they want to trace back to its origin, they correlate the serial number with your purchase, or most recent printer driver update and ISP records. Do you really think they do not have that, as part of their dragnet operations of (mobile) phone traffic or cloud storage, etc.?
Of course that only 'proves' that the document was printed with that printer, not that
you printed it, but that's now for you to disprove ...
And for what purpose would the government want to do this?
Ask them ... , 'Patriot' act? Ever hear about
'Prism'?
Cheers,
Bart