Hi,

My solution was to load the media item in an XPathNodeIterator by calling umbraco.library.GetMedia(). This way I can get the complete XML representing the media item. The TextstringArray XML is in there as <aliasOfTheTextstringArray><TextstringArray><values><value>...

List<String[]> values = new List<String[]>();
System.Xml.XPath.XPathNodeIterator xPathNodeIteratorMedia = umbraco.library.GetMedia(mediaItem.Id, true);

if (!String.IsNullOrEmpty(xPathNodeIteratorMedia.Current.InnerXml))
{
    var xml = new XmlDocument();
    xml.LoadXml(xPathNodeIteratorMedia.Current.InnerXml);

    foreach (XmlNode node in xml.SelectNodes("//values"))
    {
        var value = new List<String>();

        foreach (XmlNode child in node.SelectNodes("value"))
        {
            value.Add(child.InnerText);
        }

        values.Add(value.ToArray());
    }
}

Then to show the values:

<ul>
    @foreach (String[] row in values)
    {
        <li>
            @foreach(String s in row)
            {
                <p>@s</p>
            }
        </li>
    }
</ul>