I had a similar requirement for a look-ahead report on a project last year and created a custom view in 2007 in a format very similar to your example.
First, I made a custom date field titled NOW+15 using the formula Now()+15.
Then I created a custom filter filtering for finishes less than or equal to NOW+15 field.
Then I created a table to show the desired columns.
Then I created a custom view using the table and filter. When creating the custom view, if you select “show in menu” it will appear in the View menu so you can show the look ahead anytime with one click.
It’s not a report, but I found it easy to project during a meeting, or take a screenshot and send it to the team. It seemed to work well for me during the time I used it.
When you want 4 weeks, you can just change the 15 to a 20 in the date field. Email me if you’d like more detailed steps on creating the “look ahead” custom view.