POST request return 400 Bad request

This will be difficult to diagnose, since 400 Bad Request response, indicates that the server cannot or will not process the request due to something that is perceived to be a client error.

Saying that, it looks like your JSON is incorrectly formatted (shown in red),

'{"extIsId":"abc/777","productCode":"ExterniKodSort","name":"TA_API777","type":0,"measurementUnitCode":"KS","weightGross":1.1,"weightNett":1.1,"grossDimension":{"height":1.1,"width":1.1,"depth":1.1,"volume":1.1},"pictureUrl":"www.aaa.cz/SORT.png","expirationMandatory":1,"serialNumbersRecords":{"inboundMandatory":1,"outboundMandatory":1},"batches":1,"barcodes":[{"barcode":123456,"active":1,"default":1,"measurementUnitCode":"ks"}]}surementUnitCode":"KS","warehouseCode":"3S20","weightGross":10.5,"weightNett":9.5,"grossDimension":{"height":2,"width":1.5,"depth":3.5,"volume":10.5},"pictureUrl":"","expirationMandatory":1,"serialNumbersRecords":{"inboundMandatory":1,"outboundMandatory":1},"batches":1,"barcodes":[{"barcode":"EAN80","active":1,"default":1,"measurementUnitCode":"KS"},{"barcode":"EAN81","active":1,"default":0,"measurementUnitCode":"KS"}]}';