There isn't a capability specific to code snippets, access to the whole Toolset settings requires the 'manage_options' capability. Of the standard roles, only administrators have this capability.
Thank you very much for looking into this for me, it's appreciated!
When I create a custom user role and enable "manage_options", this always give an error when trying to update or modify custom code snippets. It's only when "delete_users" is enabled that this seems possible.
I am guessing that this shouldn't be the case then?
If I go to Toolset > Access Control > Custom Roles and enable advanced mode so that I can modify the built-in roles, then edit the author and grant them manage_options capability that is all that is required for them to be able to add/edit code snippets.
They don't have the delete_users capability.
I also created a custom role, initially copying over the author permissions and then updating them to include manage_options, and I got the same result.
If needs be I can create a sandbox site to demonstrate what I've described in my testing, but that won't help you identify what's different on your end.
I'm not going to have enough time to set this up and test it for a while, so i'll close it for now and open a new ticket if I find the same issue in the future.