I honestly don't think you can do it without corn and remain cost effective. May I ask what specific problem do you have with the corn? I understand the soy free, but you can buy quality corn that is free of chemicals and grown responsibly. If glyphosate is what you are trying to avoid, then beware of most wheat as well.
We have a feed recipe, but it contains corn and soy so it probably won't be very much help to you, but maybe it will give you an idea of some of the ingredients you may want to consider and what it takes to build a feed of your own. Some simple calculations would be required to substitute the corn and the soy for other ingredients. The important factor is the protein and starch content of those two ingredients, make sure to replace them with equal amounts of starch and protein.
Full disclosure: I did not create this recipe, someone much smarter than I am did

The creator of the recipe notes that a full balance in the diet is important as true health requires more than just a life-sustaining minimum.
Recipe for chicks. We add more corn as the protein needs change. (Percentage by weight)
Corn 52%
Roasted soy beans 29% (I know, corn and soy..)
Crimped oats 11%
Feed grade limestone 1%
Fertrell Nurtribalancer 3%
Fish meal 3.5%
Kelp meal 0.5%
Probiotics 0.1%
I used this recipe for several years, and then I moved and it was easier for us to buy bagged feed by the pallet so we aren't feeding this right now, but I would like to get back to it in the future because it works well and if you can get the ingredients, it's very economical.