Using @Eduard Lebedyuk  suggestion, I implemented it like this

Method BillingDocumentRequestRequestIn(pRequest As ARInvoices.Request.BillingDocumentRequestRequestInRequest, Output pResponse As ARInvoices.Response.BillingDocumentRequestRequestInResponse) As %Library.Status
{
  Set tSC = ..Adapter.InvokeMethod("BillingDocumentRequestRequestIn",,pRequest.MessageHeader,pRequest.GlobalParameters,pRequest.ActionControl,pRequest.BillableDocument)  Quit:$$$ISERR(tSC) tSC
  Set tSC = pRequest.NewResponse(.pResponse)  Quit:$$$ISERR(tSC) tSC
  Set StatusCode = ..Adapter.%Client.HttpResponse.StatusCode
  $$$TRACE(StatusCode)
  Quit $$$OK
}

Thanks Eduard, I understand how to do this in a http outbound but not in a SOAP one. Below is the code for the Operation. I want to get the StatusCode from pResponse. I've generated the Response class from the WSDL file and it has no properties, which is intentional.

Would I need to add a property to the response for the StatusCode?

Method BillingDocumentRequestRequestIn(pRequest As ARInvoices.Request.BillingDocumentRequestRequestInRequest, Output pResponse As ARInvoices.Response.BillingDocumentRequestRequestInResponse) As %Library.Status
{
  Set tSC = ..Adapter.InvokeMethod("BillingDocumentRequestRequestIn",,pRequest.MessageHeader,pRequest.GlobalParameters,pRequest.ActionControl,pRequest.BillableDocument)  Quit:$$$ISERR(tSC) tSC
  Set tSC = pRequest.NewResponse(.pResponse)  Quit:$$$ISERR(tSC) tSC
  Quit $$$OK
}

Thanks Robert, that's the correct answer. I just had to pass in an argument.

do output.XMLExportToString(.xml)
$$$TRACE("output :"_xml)