When you sold the house for $250,000, you may actually have a small loss based on the above.
The estate's basis in the house is the fair market value (FMV) of the house on the date of death. IF the house was sold within a year of the date of death, you can argue that the sales price was the FMV at the date of death, unless in the period of time between the date of death and the sale had some major fluctuations in the real estate market.
So if you take the sales price, subtract the basis, and then subtract the closing costs, you usually have a small loss. In your case, $223k sales price - $223k basis, less closing costs (I am assuming the difference between the sales price and the cash to distribute is qualified closing costs) gives you a loss of $16,460.01 do be divided between the 4 of you.
I hope this answers your questions. If you have any more, please feel free to ask and I will be happy to answer.
Thanks! Have a great week!