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Your code is almost there, probably you need the following:
from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
f=DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)()
R.<X> = PolynomialRing(GF(13))
Y.<t> = R.quotient(X^1024 + 1)
Y(f)
Here you obtain
10*t^7 + 5*t^6 + 3*t^4 + 7*t^3 + 12*t^2 + 2*t + 1
