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Income Taxes - Additional Information (Detail) - USD ($)	Jun. 30, 2023	Sep. 30, 2022
IncomeTaxes [Line Items]
Valuation Allowance	$ 0	$ 0

X

- Definition

IncomeTaxes

+ References

No definition available.

+ Details

Name:	genc_IncometaxesLineItems
Namespace Prefix:	genc_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=121826272&loc=d3e32537-109319

+ Details

Name:	us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant