Typical references say dirt weighs 120 lb per cu ft. That's for compacted and saturated soil. There are lighter mixes meant for rooftop gardening that weigh 50 lb per cu ft when saturated.
http://www.greenrooftops.com/Planning_Soil.aspx
So, assuming planter box is 1 ft deep, 150 sq ft of planter box = 150 cu ft dirt = 18.0K lbs if using regular dirt or 7.5K lbs if using light-weight mix.
Either way, this would become (IMO) something for a professional to design and maybe to build.
Access might be via stairs, or even spiral stairs. Certainly need better than a ladder. For water, could plumb to a hose bib on the platform and/or use drip irrigation.