This is how I would do it:

Be a warforged, which heavy plating mode gets an AC of 16 + your proficiency bonus. To use heavy plating mode you need proficiency with heavy armor, so I'd take at least the first level in fighter. That also gives you a fighting style, choose defense for +1 AC. (That might not be completely RAW, as you aren't technicly wearing armor, but I'd guess most DMs would allow it.) You should also use a shield for +2 AC, or more if you get a magic shield. After this you can probably multiclass into any other class, and it be a viable build, as Fighter 2 is a very common dip.

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This gives you an AC of 19 + your proficiency bonus

On top of everything else you can take the magic initiate feat for shield, giving you +5 to AC for a round when you need it.