A portfolio does need to be at least somewhat visual. My original UX design portfolio consisted entirely of text. (At the time, the portfolio site itself was also the only item in my portfolio!) Text is, not surprisingly, not the best way to communicate what I have done on my interaction design and visual design projects. When I met with the CEO of another design company, his first reaction upon seeing my portfolio was that I needed to build it around images.
However, your assumption that a portfolio of only screenshots would show off the work of only the designer is correct - at least as a first impression. Most people spend only a few seconds on a webpage, so that first impression may stay with them.
I've been a member of Behance for most of the time I've been in business. I notice that Behance's featured work is biased towards the visually stunning. People who are great artists or great graphic designers - and I am not - get great exposure on Behance. Information architects and interaction designers are less likely, because their work is like a developer's: the real magic is behind the scenes. (Within UX, there is a concept of emotional design - one tenet of which is that products that look nice are more likely to be perceived as user-friendly even if they are not. I suspect that's in play here.)
As a developer, code samples are important to show the quality of the code that you write. But there are other important factors:
You need to show that your code works. I would recommend linking to
a live site and/or the app's listing in the App Store. If it is not
available there, record a screencast video with a tool such as Jing
to explain your process and how you worked.
You need to show that your code is of high quality. If you can share the code with people, I would recommend linking to a
GitHub account. Let people see your process - what you do for
changesets, what you do for unit testing.
Show that you are good at working with others. Have testimonials
from clients and, where possible, others on your project team. If
you can get a testimonial from the designer of one of your apps, that
makes it clear that 1) you do good enough work for the designer to
recommend you, and 2) you didn't do the design work for the app.
A lot of people think now that developers are designers. There is a lot of overlap in job descriptions on both sides now.
So to make it clear that you do not do UI or UX design work, I would recommend including a list of services rendered with each project. It can be as simple as "Design", "Development", "Project Management", etc. Or if you want to also include languages you worked with, that is probably fine for a development portfolio as well. (For a design portfolio, I haven't found that people care about which responsive frameworks I use - but if I were still a developer seeking dev work, people absolutely would care!) If your portfolio site is a WordPress site with portfolio capabilities, you may be able to specify categories and have a list of projects that can be filtered according to the kind of work you did.
Personal programming projects are fine to include in portfolios. You don't have to say that they were personal or unpaid. Just present them like any other project. I know of professional designers who have done design work as employees of Facebook, but they have still included personal projects in their portfolios. Personal projects show that you love what you're doing enough to spend at least some of your personal time advancing your skills.
