Welcome
@bludwig !
You could very easily convert your tub filter into a bog by adding gravel and plants - no more filter mats to clean! More on that if you're interested!
Anyway - your pond is on the small side for the number of fish you are housing. Initially 12 small koi may not seem like a lot in a pond that size, but as they grow, the amount of waste they produce grows by leaps and bounds. There's no real "formula" for how many koi you should keep in a pond, but the standard advice is 1000 gallons for the 1st koi; 250 - 500 gallons for each additional. A lot depends on the type of filtration you have on the pond, but water quality with koi can turn bad very quickly. I don't know if that's what happened to your fish, but it's certainly not uncommon for fish in an established pond to suddenly start dying when the biomass exceeds the ability of the filter to keep up.
Having said that, pea soup water is not an indication of poor water quality, but it does point to too many nutrients in the pond that are not being consumed by either the filter or the plants. This is especially true in spring before the plants start to grow. Water changes do not address this issue - in fact they may actually make it worse. Your pond is trying to find equilibrium - every time you add fresh water, that process starts over.
Getting more plants in the pond will be the most helpful, so that may require some patience. As someone else said - the green water is of no consequence to the fish. They don't mind it and it is in fact doing its part to keep the pond healthy.