This is quite a common mistake in English (indeed, there are two mistakes)

1. ‘together’ does not go in the the middle of the clause, but the beginning or end (usually the end)

2. ‘we go’ doesn’t have a tense or modal. It should be past/present/future, or have a modal such as ‘let’s’ or ‘can’.

People usually mean ‘let’s go together’ or ‘we can go together’.