Need help framing a loft in a pole barn

I have an outbuilding/garage that is 12x24x14 (HxLxW). It is constructed with 2x6 wall framing from 4x4 posts. Using 2x12 wood I-Frames the loft will be 12x14 in size.
My question is I was going to make a 12x12x14 frame and then hang the I-Beams inside that once in place but my question is attaching that frame to the barn/garage sides.
Can I just lag bolt the frame to the 4X4's or do I need to also run a 2x4's down the side of each 4x4 under the frame for extra support or should I double the 4x4's?
I plan on drying cedar up there and then use it for storage.

Here is a pick of the framing to give you an idea of the structure:


In case there's confusion in my description here's a synopsis:
The I-beams (joists) are wood, 2x12 size.
I will basically make a frame (12x14) to hang those joists in and then attach the frame to the wall with lag bolts into each 4x4 corner.
Question is - in the 4 corners where the current 4x4's are for the building, do I just (supplement) run a 2x4 down in each corner to support the frame for the joists or does each of the 4 corners need another 4x4.
Then, in the 12 foot span holding this frame along the side of the building, does the frame for the joists need supports running down to the floor? I'm thinking I do @ 6' and it should be a 4x4.
So 2 questions, one about supporting the corners and one about supporting the sides.
Thanks for your time and apologies for not being clearer.

 

What is under the existing 4x4s that support the current structure? What kind of footings are there? Everything depends on that. Support if from the bottom up.