Here is a link to another thread started by one of our members, showing her 55g planted tank with the same light fixture you have (2 18-inch T8 tubes). As you can see, it is possible. http://www.tropicalfishkeeping.com/a...pgrade-113536/
One has to select plant species carefully, as has been mentioned already. And I agree with what others have said about the various plants.
Good tubes will help, and as noted in the linked thread, she is using Life-Glo which are about the best in this situation. They should be replaced every 12-18 months. UltraSun made by ZooMed is about the same, and slightly less expensive.
If you decide to upgrade to open your options a bit, the next step would be a single 48-inch T8, but that would only be minimally above what you now have, so if upgrading is decided, I would go one better and get a dual-tube 48-inch T8. Do not get T5, that is much more intense lighting and will cause other problems.
Glass cover sets are made for the standard sized tanks; the glass sits down on the inside lip around the frame. The light fixture then sits on top of the frame (end to end) so it is not actually touching the glass cover which could fall into the tank if it was. I have this arrangement on my 4 and 5-foot tanks.