The 'What's the Highest Score an NFL Team Could NOT Earn in the Super Bowl?' Puzzle

I am not nearly as interested in the Super Bowl as my kids.  One thing I do enjoy is trivia or number challenges. Here is a combination of the two: a football number challenge.

What is the HIGHEST score an NFL team could NOT in the Super Bowl while playing on offense (meaning no Safeties, which is a defensive score). Assume that there is NO TIME LIMIT to this game.
The only ways to score are:

• TOUCHDOWN
• FIELD GOAL
• 1-EXTRA-POINT CONVERSION (can only be earned after a touchdown)
• 2-EXTRA-POINT CONVERSION (can only be earned after a touchdown)

No Googling the answer, as I am certain someone has already worked it out. Instead, see how close you can get. I will be working on it as well, as I do not yet know the answer.

Post your answer in the COMMENTS, and I will keep them hidden for some time so everyone can try it out for themselves.