Yes! The same trick that you can use with k <= 32 also works with longer k. The difference is just that the result doesn’t fit in a single machine word any longer, and so some of the bit-twiddling operations become a bit more complex. For example, most modern hardware supports 128-bit integers (and many modern languages, like Rust) expose this type natively. You can pack k <= 64 bits into a 128-bit integer.

Beyond that, or more generally, one typically uses an array of bytes of the minimum required size. Each byte is 8 bits and can hold 4, 2-bit encoded nucleotides. So if you need a 37-mer, say you could pack it into 10 bytes. Many tools have this type of capability. For example, you can take a look in the source code of KMC, or in the Kmer class from the Cuttlefish tool developed in my lab (e.g. here).