Family #73 in the 1767 Grimm census.
Family #147 in the 1775 Grimm census.
Family #103 in the 1798 Grimm census.
Georg Koch was a Lutheran farmer from Darmstadt. He immigrated to Russia with his wife Juliana on travel document number 4061.  The couple departed from Luebeck on the Pink Slon and arrived on 18 June 1766.  A Pink was a small, flat-bottomed ship with a narrow stern, typically square rigged and used to sail short distances and/or in shallow waters.  The Slon on this journey was commanded by Lt. Sergey Panov. 
The couple is listed in the 1767 Grimm census along with a one-year-old son Johann Adam. Their son must have been born in St. Petersburg or Oranienbaum, Russia shortly after their arrival in Russia. The village of Grimm was settled in July of 1767, so we can estimate their son's birth month as around July of 1766, after they arrived in Russia, but before they arrived in Grimm.
In that same document, Georg is described as a Lutheran craftsman from Darmstadt.  That is not necessarily his birth town, but rather the last town he lived in prior to immigrating to Russia. Darmstadt is a good starting point when searching for birth places, so I will leave it as such until we can determine the exact location through an official birth record.
1767 Grimm Census 
At the time of the 1775 census, the couple had two children:
Not only is the name of his son different from the name of the son listed in the 1767 census, but their birth years are off by 3 years. This most likely signifies that the eldest son, Johann Adam, passed away before 1775.
There is also a discrepancy with the age of his wife, Juliana. In the 1767 census, she was 1 year younger than her husband; in the 1775 census, she is 9 years younger. Unfortunately her age is not listed in the 1798 census, so a comparison can't be done. Her last name at birth is also not listed in the 1798 census, so it will be difficult to confirm through a German birth or marriage record.
1775 Grimm Census 
Georg Koch is not specifically listed in the 1798 census, but his wife is listed as a widow, living with their son Johannes. Georg must have died between 1775-1798.
1798 Grimm Census 
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