How to refactor this groupby alike method but with index?
First of all get rid of these tuples. After one week you will forget what each int represents. Define simple struct/class for your brick.

Second thing, small performance suggestion for big row count - explicit initial list size:

... = new List&lt;Tuple&lt;char, int, int, int&gt;[]&gt;(myBoard.Length);//assuming myBoard is an array


without it, list would be recreated and rewritten every 4 new elements.

Below is mine implementation with linq extensions. Probably it is not faster. I don't know if it is more readable, but at least line count is smaller :)

public struct Brick
{
    public char Symbol { get; set; }
    public int Length { get; set; }
    public int RowID { get; set; }
    public int ColumnID { get; set; }

    public override string ToString()
    {
        return string.Format("{0} {1} {2} {3}", Symbol, Length, RowID, ColumnID);
    }
}

public Brick[][] GetHorizontalBricks(char[][] board)
{
    return
        board
            .Reverse() //bottom up row order
            .Select((row,rowIndex) =&gt;
                row
                    .Select((c,i) =&gt; new { c = c, i = i })
                    .GroupBy(symbol =&gt; symbol.c) //assumption that we will never see 2 groups of same nonzero character in single row
                    .Where(symbol =&gt; symbol.Key != 0 &amp;&amp; symbol.Count() &gt; 1)
                    .Select(brick =&gt;
                        new Brick
                        {
                            Symbol = brick.Key,
                            RowID = rowIndex,
                            ColumnID = brick.First().i,
                            Length = brick.Count()
                        })
                    .ToArray()
            )
            .Reverse() //reverse again to show result in form like you provided
            .ToArray();
}


and Console app test:

static void Main(string[] args)
{
    char[][] board = new char[][]
    {
        new char[] { (char)0, (char)0, 'b' ,'b','b','c'},
        new char[] { (char)0, (char)0, 'h' ,'g','g','c'},
        new char[] { (char)0, (char)0, 'h' ,'a','a','c'},
        new char[] { (char)0, (char)0, 'f' ,'f','d','d'},
        new char[] { (char)0, (char)0, 'i' ,'j','e','e'},
        new char[] { (char)0, (char)0, 'i' ,'j',(char)0,(char)0}
    };

    foreach (var row in new Program().GetHorizontalBricks(board))
    {
        Console.WriteLine("Row:");
        foreach (var brick in row)
            Console.WriteLine(brick);
    }

    Console.ReadLine();
}