There is a John Schmitt in the 1840 DC Census listed with a wife in her 20's and child under 6.
This marker at first appeared to me to say aged 51 with a year of death in the 1860's. Also the area of the cemetery is consistent with that. However multiple photo that I have added may even be as wide as aged 31 in in 1845. Adding in a possible match with census my guess would be consistent with that since he is in section 2. 1814 - 1845 aged 31, or 1814 - 1865 aged 51. 1809 - 1860 window for now.
Holy Rood Cemetery
District of Columbia
District Of Columbia, USA
Plot: Section 2
Created by: Michael [Randy] Walsh
Record added: Jan 20, 2013
Find A Grave Memorial# 103866709