Redirecting C# compilation errors to a text file

Hello.
I'm completely new to Unity and encountered an issue while writing a small editor customization.
I would like to capture C# compilation errors that attached scripts caused and redirect the messages to a text file. I found the LogMessageReceived-family callbacks, but it doesn't seem to capture CSxxxx errors. Is there any way to do this, or am I doing something wrong? Debug.Log() can be captured just fine.
Here's the minimum code:
//Assets/Editor/UnityAccessibility.cs
using UnityEngine;
using UnityEditor;
[InitializeOnLoad]
public class UnityAccessibility{
static UnityAccessibility(){
Application.logMessageReceivedThreaded += WriteUnityLog;
}
private static void WriteUnityLog(string logString, string stackTrace, LogType type){
System.IO.File.AppendAllText("C:\\git\\a.txt",type.ToString()+" : "+logString+'\n');
}
}
Sorry for some tentative hard-codings.