As per the Odessa Library Collection, the Axtmann surname shows up in Baden > Odessa. German roots were likely Alsace-Lorraine = Reichsland> Elsass-Lothringen.http://www.odessa3.org/
Baden was founded in 1808 in Kutschurga district > Kherson gubernia. (Baden was technically in Bessarabia.) In 1859 there were 149 homes there. In 1943 there the population was 2,186.
Today called Lymanske. Lymanske (Лиманське in Ukrainian) is a town in the Rozdilnianskyi raion/district of the Odessa Oblast in Ukraine. It is located along the east side of the Kuchurhan Reservoir on the border with Transnistria in Moldova.
A village called Selz (named after Seltz in Alsace) was established at this location along the Kutschurgan Liman in 1808 by Roman Catholic German and Alsatian (French citizens) immigrants to the Kutschurgan Valley, then part of the Russian Empire. It received its present name after the remaining German residents were driven from the area by the advancing Soviet army in 1944. The former German villages of Baden and Kandel located just to the north and south, respectively, of Selz have been absorbed into the current Ukrainian town.
1944 map of Badenhttp://www.blackseagr.org/maps/Baden%201944%20Map.jpghttp://www.grhs.org/chapters/krig/villages/baden_odessa.htmhttp://www.blackseagr.org/learn_odessa.htmlhttp://valery-mock.livejournal.com/26837.html
The Creator of following link, a published author, shares your Kutschurga district heritage. Records Section is well organized and clearly explained http://www.goldade.net/index.htm