matevijay,

Just in case you'd like a macro solution, this one will produce 10000 unique alphanumeric entries very quickly and put them in column A of the active sheet starting in A1. I did use shg's method for getting a random alphanumeric character. I did my best to make it customizable. For a different number of results, change the (1 to 10000) in the Dim arrUnqAlphaNums line to be (1 to x) where x is the desired number of results. To change which characters can be used for your alphanumeric strings, change the strCharacters to only include the characters desired.
Sub tgr()
    
    Const strCharacters As String = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    
    Dim cllAlphaNums As Collection
    Dim arrUnqAlphaNums(1 To 10000) As String
    Dim varElement As Variant
    Dim strAlphaNum As String
    Dim AlphaNumIndex As Long
    Dim lUbound As Long
    Dim lNumChars As Long
    Dim i As Long
    
    Set cllAlphaNums = New Collection
    lUbound = UBound(arrUnqAlphaNums)
    lNumChars = Len(strCharacters)
    
    On Error Resume Next
    Do
        strAlphaNum = vbNullString
        For i = 1 To 16
            strAlphaNum = strAlphaNum & Mid(strCharacters, Int(Rnd() * lNumChars) + 1, 1)
        Next i
        cllAlphaNums.Add strAlphaNum, strAlphaNum
    Loop While cllAlphaNums.Count < lUbound
    On Error GoTo 0
    
    For Each varElement In cllAlphaNums
        AlphaNumIndex = AlphaNumIndex + 1
        arrUnqAlphaNums(AlphaNumIndex) = varElement
    Next varElement
    
    Range("A1").Resize(lUbound).Value = Application.Transpose(arrUnqAlphaNums)
    
    Set cllAlphaNums = Nothing
    Erase arrUnqAlphaNums
    
End Sub


And just in case...
How to use a macro:
  1. Make a copy of the workbook the macro will be run on
    • Always run new code on a workbook copy, just in case the code doesn't run smoothly
    • This is especially true of any code that deletes anything
  2. In the copied workbook, press ALT+F11 to open the Visual Basic Editor
  3. Insert | Module
  4. Copy the provided code and paste into the module
  5. Close the Visual Basic Editor
  6. In Excel, press ALT+F8 to bring up the list of available macros to run
  7. Double-click the desired macro (I named this one tgr)