Any way to load code from a file and highlight it?

I’m interested in adding code snippets with syntax highlighting to my Jekyll site. Obviously the following works fine,

```lang
some code here
```

where lang is the language I want. However, I would like to load code from an external file, so that I can change it easily. This is simple enough to do with a little bit of Javascript and HTML, like this

<script>
fetch('url_here')
.then(response => {
    return response.text();
})
.then(text => {
    document.getElementById("demo").innerHTML = text;
})
</script>
<pre><code id="demo"></code></pre>

but the code comes out without syntax highlighting, presumably because Jekyll/Liquid does not evaluate the contents of <code>. If I put this in a markdown codeblock or use {% highlight %}, like so

```lang
<pre><code id="demo"></code></pre>
```

I literally get <pre><code id="demo"></code></pre>, not what it evaluates to. Any ideas how I can achieve what I want?

Thanks!