Not an answer to your question but a reference method to compare your results with:

• Read this PostGIS document http://postgis.net/docs/ST_Length.html
• Take the Geography example "Return length of WGS 84 geography line" and insert your linestring into the query

SELECT ST_Length(the_geog) As length_spheroid,  ST_Length(the_geog,false) As length_sphere
FROM (SELECT ST_GeographyFromText(
'SRID=4326;LINESTRING ( 37.6232398 55.7615482, 37.6262633 55.7606701, 37.6232398 55.7615482, 37.6262633 55.7606701, 37.6232398 55.7615482, 37.6262633 55.7606701)') As the_geog)
As foo;

Check the results:

length_spheroid 
1067.52749423872

length_sphere
1064.36864138641

I also converted the data into EPSG:32637 with OpenJUMP and measured the distance: 1067.1980.

Conclusion: Distance measured from Google maps is not a good reference.

Not an answer to your question but a reference method to compare your results with:

• Read this PostGIS document http://postgis.net/docs/ST_Length.html
• Take the Geography example "Return length of WGS 84 geography line" and insert your linestring into the query

SELECT ST_Length(the_geog) As length_spheroid,  ST_Length(the_geog,false) As length_sphere
FROM (SELECT ST_GeographyFromText(
'SRID=4326;LINESTRING ( 37.6232398 55.7615482, 37.6262633 55.7606701, 37.6232398 55.7615482, 37.6262633 55.7606701, 37.6232398 55.7615482, 37.6262633 55.7606701)') As the_geog)
As foo;

Check the results:

length_spheroid 
1067.52749423872

length_sphere
1064.36864138641

I also converted the data into EPSG:32637 with OpenJUMP and measured the distance: 1067.1980.

Conclusion: The distance that you measured from Google maps is not a good reference. Are you sure that you measured that distance five, not six times? With five times it would make 1040.291 which is much closer to results with EPSG:32637 and with geography.