Am I able to give each participant a specific code
If you hand over a printed code, and the respondent has to type it, the access links will probably be too long. If you had a bit more time and respondentes used mobile devices, you could create an QR code from each access URL - but if I interpret the sparse information correctly, this will not be a valid option.
Therefore, serial numbers will be the codes to use here. The question now is how to handle privacy.
I need to be able to work out which participants to follow up with an interview after the survey is analysed.
There are (at least) two options. I assume that the choice for a follow-up is based on the responses in the (screening?) questionnaire.
Option 1: You could simply create a list who got which code (serial number). Keep this list in a safe, and the risk is quite limited.
Option 2: You could have each respondent draw a code (from a box or whatever), so that you do not know who belongs to which code. Then, in the questionnaire, use value() and a few formulas to check if the respondent is eligable for the follow-up questionnaire. If this is the case, use an "opt-in" question to ask for the email address (privacy mode pseudonymous) or use the email to personal contact question (if you really want is anonymously) to send the respondent the link to the follow-up questionnaire.
Option 2 requires an automated evaluation if the respondents shall do the follow-up questionnaire. If this is not possible (due to qualitative aspects, for example), only option 1 is possible.