Unless you have a large budget, alternatives to having a person (or group of people) parse the data are potentially complex and unreliable.
Card Sort a Folksonomy
Card sorting is a simple technique in user experience design where a
group of subject experts or "users", however inexperienced with
design, are guided to generate a category tree or folksonomy.
A folksonomy is a system of classification derived from the practice
and method of collaboratively creating and translating tags to
annotate and categorize content; this practice is also known as
collaborative tagging, social classification, social indexing, and
Depending on your results and expertise, this initial card sorting is something you can probably do alone. If, however, you need to take a more qualitative approach (e.g. you need to give scores to, or add weights to answers) it's advisable to work in a group.
In that case, try to get 3-5 people in a room with a projector and and whiteboard. Pull up the answers and start parsing. Discuss what you think the core point of an answer is and decide what category that might belong in. Initially, for the sake of speed, you can just focus on naming your categories. As you parse more answers the names and numbers of your categories will evolve.
The outcome of a session like this could be that you've categorized all your answers and are are ready to start putting the results to use (e.g. in a presentation), or you may just have decided on a list of categories and potentially a scoring rubric that can be handed off to someone else to use in the processing of the data.