Mira and Jay Patel bought their home in $2003$ for $$226,000.$ Jay, her husband, died $18$ months ago. When Jay died $18$ month ago, the home was valued at $$600,000$in his estate paperwork. Today it will sell for $$720,000.$ The realtor charges $6\%$ commission on the sale. She and Jay qualify for a Section $121$ exclusion. What is Mira's recognized gain on the sale. Please show your calculations.