With Gusmans reminder I created a method to extract the response from the WebException:
public static string ParseExceptionRespose(WebException exception)
{
string responseContents;
Stream descrption = ((HttpWebResponse)exception.Response).GetResponseStream();
using (StreamReader readStream = new StreamReader(descrption))
{
responseContents = readStream.ReadToEnd();
}
return responseContents;
}