The most complete record of Confederates buried in the Cedar Hill Cemetery (the Vicksburg City Cemetery) that I am aware of is “Confederate Roll of Honor, Known Confederate Dead, Vicksburg Campaign, January 1862-July 1863," compiled by Gary W. Webster, “Ole Sow” Publications, 1998.

By far, the vast majority of the listing contain no information on rank. Here are the few Field Grade Officers that I find, along with the date of death:

Anderson, J. B., Major, [Partisan Rangers], May 19, 1863
Jo[seph C.] Boyd, Major, 3rd Tennessee, June 12, 1863
R. B. Campbell, 40th Mississippi, June 28, 1863
[Isham W.] Garrett,** Col./BGen., 20th Alabama, June 17, 1863
M[artin] E. Green, MGen.[BGen.], Missouri, June 27, 1863
S.H. Griffin, Lt. Col., 31st Louisiana, June 27, 1863
[Frederick W.] Hoadly, Major, 1st Tennessee Heavy Artillery,
June 9, 1863
T[homas] C. Humble, Major, [31st ] Louisiana, January 7, 1863
[L. L.] McLaurin, Lt. Col., [27th Louisiana], June 24, 1863
W. C. Timmons, Lt. Col., 2nd Texas, June 26, 1863, buried by the
side of Lt. Col. Hamelton
T.[F.?] M. Tucker, Major, _________, December 31, 1862

...

** 06 17 1863 [Wednesday]

Early in the day Colonel Garret [Garrott], 20th Alabama, was shot dead through a porthole in our fortifications by a Yankee sharpshooter. (Isaac Stamper, diary, Fife Major, 43rd Tennessee Infantry)