これで十分だろ
Class Hoge
    Public Sub New()
        SetInstanceCode()
        ' 略
    End Sub
    Public Sub New(ByVal a As String)
        SetInstanceCode()
        ' 略
    End Sub

    ' 略

    Private instanceCode As Integer
    Private Shared Counter As Integer = 0
    Private Sub SetInstanceCode()
        Me.instanceCode = Counter
        Counter += 1
    End Sub
End Class

でも >>628 に同意