In general the computation of the weight enumerator of a code is hard and even harder so for the coset leaderweight enumerator. Generalized Reed Solomon codes are MDS, so their weight enumerators are known andits formulas depend only on the length and the dimension of the code. The coset leader weight enumerator ofan MDS code depends on the geometry of the associated projective system of points. We consider the cosetleader weight enumerator ofFq-ary Generalized Reed Solomon codes of lengthq+ 1 of small dimensions,so its associated projective system is a normal rational curve. For instance in case of the [q+ 1,3, q−1]qcode where the associated projective system of points consists of theq+ 1 points of a plane conic, theanswer depends whether the characteristic is odd or even. If the associated projective system of points of a[q+ 1,4, q−2]qcode consists of theq+ 1 points of a twisted cubic, the answer depends on the value of thecharacteristic modulo 6.