The given sentence is okay. The writer is trying to make a point here by emphasizing the color grey. That is, the sign was grey, and the school building was grey, implying that that the school itself was "grey," that is, stodgy, dull, pedantic.
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CliveAn academy is a school, so the name should just be'"Redlands Academy for Girls"Perhaps the writer meant that the sign said '"Redlands Academy, School for Girls" ... like this:
I'm just guessing.Redlands Academy
School for Girls