Segment Information (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2024 USD ($) state region	Mar. 31, 2023 USD ($)	Mar. 31, 2024 USD ($) state region segment	Mar. 31, 2023 USD ($)	Sep. 30, 2023 USD ($)
Segment Reporting Information [Line Items]
Number of states in which home building segments operate | state	13		13
Number of regions in which entity operates | region	3		3
Number of reportable segments | segment			3
Revenue	$ 541,540	$ 543,908	$ 928,358	$ 988,836
Operating income	35,991	38,792	56,256	67,294
Depreciation and amortization	3,573	3,020	5,806	5,533
Capital expenditures			11,501	7,824
Assets	2,515,410		2,515,410		$ 2,411,033
Gain on sale of investments	8,600		8,600
Operating Segments
Segment Reporting Information [Line Items]
Operating income	69,265	73,274	113,100	130,572
Depreciation and amortization	3,126	2,725	4,966	4,933
Corporate and unallocated
Segment Reporting Information [Line Items]
Operating income	(33,274)	(34,482)	(56,844)	(63,278)
Depreciation and amortization	447	295	840	600
Capital expenditures			3,301	2,574
Assets	552,993		552,993		739,986
West
Segment Reporting Information [Line Items]
Revenue	347,338	330,413	584,431	605,228
West | Operating Segments
Segment Reporting Information [Line Items]
Operating income	46,030	45,513	74,369	82,870
Depreciation and amortization	2,452	1,939	3,763	3,544
Capital expenditures			6,873	3,086
Assets	1,157,508		1,157,508		994,597
East
Segment Reporting Information [Line Items]
Revenue	111,844	120,071	186,621	206,261
East | Operating Segments
Segment Reporting Information [Line Items]
Operating income	12,282	16,244	18,638	25,506
Depreciation and amortization	406	388	615	661
Capital expenditures			865	1,239
Assets	432,585		432,585		356,020
Southeast
Segment Reporting Information [Line Items]
Revenue	82,358	93,424	157,306	177,347
Southeast | Operating Segments
Segment Reporting Information [Line Items]
Operating income	10,953	11,517	20,093	22,196
Depreciation and amortization	268	$ 398	588	728
Capital expenditures			462	$ 925
Assets	$ 372,324		$ 372,324		$ 320,430