This article considers a strongly regular graph with parameters (2048,276,44,36) that is related to the extended binary Golay code. That graph is known since about 1975 but there seems to be not much information on the contained maximal cocliques. The source package of this article contains a data file that encodes a sequence of maximal independence sets of that graph, covering all sizes from 20 to 67 and the size 72, and a Pascal program to check this assertion and to optionally generate a text file (to be read by the computer algebra system GAP) that contains the adjacency lists of that graph and the list of the independence sets.