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R.<x> = GF(2)[]
[ p for p, mul in factor( x^(2^8)-x ) if == 8 ]

This works since any element in $\mathbb F_{2^8}$ is fixed by the Frobenius morphism $x\to x^{2^8}$. The field generators are among these elements, we insist that they have the maximal degree eight (of the minimal polynomial over $\mathbb F_2$) to pick the generators among all elements. (All ignored multiplicities mul are equal to one.)

This and the other answers show how versatile is sage, and how it supports thinking and experimenting.