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Perhaps, you want a free module rather than span:

R.<X>=PolynomialRing(GF(2))
FreeModule(GF(2), [X^(2^j) for j in range(3)])

Perhaps, you want a free module rather than span:

R.<X>=PolynomialRing(GF(2))
FreeModule(GF(2), [X^(2^j) for j in range(3)])

which gives

Free module generated by {X, X^2, X^4} over Finite Field of size 2