I too have an interest in the High Street, I have a Mary Henderson born at no. 37 in 1880, is it still there?
" Courant Court: High Street, North side, No. 37, Site of the Elgin Courant Newspaper Offices and Printing Presses and home to 4 families in 1851, and 7 families by 1901. In 2002 it is a gated close with a square pend, the houses bieing 3 storey at the pend and becoming 2 storey further down the close. There is evidence of bricked up doors and windows on the right hand side, including one large bricked-up access area witha hoist in the roof above which was probably connected with the old Elgin Courant Newspaper Printworks"
From The Lands and People of Moray , The Closes of Elgin by Bruce Bishop. Published in 2002 by J & B Bishop, Rivendell, Miltonduff, Elgin, Moray
Hope this is helpful. This little book is available from the North East Family History Society in Aberdeen, Scotland