I have for categories example A,B,C & D and have 24 questions each with 4 possible answers.
When taking the survey I am only allowed to select one answer from the possible four answers for each question.

Each of the 4 possible answers is mapped back to one of the four categories.
Based on your answers selected I would like to calculate your highest category (#answers grouped by category)

Is this possible in LimeSurvey

You can do this using Expression manager in equation type questions.

1) The category "scores" - four equation questions, each with an expression something like:
2) The highest category - an equation question with an expression something like:

Tx's Tpartner

I'm a total newbie to limesurvey and will definitely give your advice an attempt.