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Property and Equipment - Additional Information (Detail) - USD ($)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023
Property, Plant and Equipment [Line Items]
Property and equipment (fully depreciated assets)	$ 23,365,000	$ 22,693,000
Property plant and equipment not yet placed in operation	$ 1,327,000	$ 1,295,000

X

- Definition

Property and equipment (fully depreciated assets).

+ References

No definition available.

+ Details

Name:	genc_PropertyAndEquipmentFullyDepreciatedAssets
Namespace Prefix:	genc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Property plant and equipment not yet placed in operation.

+ References

No definition available.

+ Details

Name:	genc_PropertyPlantAndEquipmentNotYetPlacedInOperation
Namespace Prefix:	genc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-7A

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration