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Property and Equipment - Additional Information (Detail) - USD ($) | 12 Months Ended
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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

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- 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

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- 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

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