Возможно, я не правильно понял ваш вопрос, но, возможно, это будет отправной точкой для вашего:
//The feedCodes (i put one in two times, to have one appearing most often)
var values = new string[] { "9051245", "9051246", "9051247", null, "", "9051245", "9031454", "9021447" };
//Just filter the list for filled up values
var query = values.Where(value => !String.IsNullOrEmpty(value))
//and group them by their starting text
.GroupBy(value => value.Substring(0, 3))
//order by the most occuring group first
.OrderByDescending(group => group.Count());
//Iterate over all groups or just take the first one with query.First() or query.FirstOrDefault()
foreach (var group in query)
{
Console.WriteLine(group.Key + " Count: " + group.Count());
}