I need to send message from the certain E-mail address (E-mail Distribution Group) with VBA code. I have permission "Send as" and I can do it by hands, changing field "From".

Use SentOnBehalfOfName, and as long as your Exchange account has SendAs permission for the shared mailbox or distribution group, it will be sent from the shared account or group, not sent on behalf of.

If you want to send from another account in your Account list, you'll use SendUsingAccount and select the account by index or by name. See Macros to send message using the default account or a specific account for code samples.

SendAs an address code Sample

Note: this macro is used with Exchange account to send from addresses you have SendAs permissions.

Sub CustomMailMessage()
 
Dim OutApp As Outlook.Application
Dim objOutlookMsg As Outlook.MailItem
Dim objOutlookRecip As Recipient
Dim Recipients As Recipients
 
Set OutApp = CreateObject("Outlook.Application")
Set objOutlookMsg = OutApp.CreateItem(olMailItem)
 
Set Recipients = objOutlookMsg.Recipients
Set objOutlookRecip = Recipients.Add("alias@domain.com")
objOutlookRecip.Type = 1
  
objOutlookMsg.SentOnBehalfOfName = "sales@domain.com"
objOutlookMsg.Subject = "Testing this macro"
objOutlookMsg.HTMLBody = "Testing this macro" & vbCrLf & vbCrLf

'Resolve each Recipient's name.
For Each objOutlookRecip In objOutlookMsg.Recipients
objOutlookRecip.Resolve
Next
 
'objOutlookMsg.Send
objOutlookMsg.Display
 
Set OutApp = Nothing
 
End Sub