With a 128K context length and 8 bit KV cache, the 27b model occupies 22 GiB on my system. With a smaller context length you should be able to fit it on a 16 GiB GPU.
Memory is needed for more than just the parameters, e.g. the KV cache.
KV = key-value
Just checked - 19 gigs with 8k context @ q8 kv.Plus another 2.5-ish or so for OS etc.