There are several possibilities here. For me the most natural are, " !t's a twenty-minute walk to the park' , 'It takes twenty minutes to get to the park on foot. or 'It takes twenty minutes to walk to the park.'
'Walking (gerund) to the park takes me twenty minutes' and 'Walking to the park (participle), it takes me twenty minutes are possibilities. The last contains a dangling participle, and many would consider it incorrect.
As regards differences in meaning, they are not particularly significant. It's a matter of personal preference.