Well I solved it with this script

$EmailFrom = "from@outlook.com"
$EmailTo = "to@gmail.com"
$EmailSubject = "Testing with attachments"  

$SMTPServer = "smtp.office365.com"
$SMTPAuthUsername = "authuser@outlook.com"
$SMTPAuthPassword = "password"

$emailattachment = "<fully qualified path and name>"

function send_email {
    $mailmessage = New-Object System.Net.Mail.MailMessage 
    $mailmessage.From = ($emailfrom) 
    $mailmessage.To.Add($emailto)
    $mailmessage.Subject = $emailsubject
    $mailmessage.Body = $emailbody
    $attachment = New-Object Net.Mail.Attachment($emailattachment)
    $attachment = New-Object Net.Mail.Attachment($emailattachment, "text/plain")
     $mailmessage.Attachments.Add($attachment)

    #$mailmessage.IsBodyHTML = $true
    $SMTP = New-Object Net.Mail.SmtpClient($SmtpServer, 587)  
    $SMTP.EnableSsl = $true
    $SMTP.Credentials = New-Object System.Net.NetworkCredential($SMTPAuthUsername , $SMTPAuthPassword) 
    $SMTP.Send($mailmessage)
    $attachment.dispose()
}

send_email

I did try using Send-MailMessage but it wasn't clear how to send the SMTP server credentials. The -credentials option seems to want to use the local server credentials

Thanks for all the suggestions