Is it possible to set tile entity data on an enderman's held block?

Is there a specific command that I can do to summon an enderman holding a command block with a custom command preset?

I tried the following command, but the command block doesn't have a command inside:

summon minecraft:enderman ~ ~ ~ {carriedBlockState:{Name:"minecraft:command_block"},TileEntityData:{Command:"time set 1000"}}

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