The Golod property of powers of the maximal ideal of a local ring

We identify minimal cases in which a power (mathfrak {m}^inot =0) of the maximal ideal of a local ring R is not Golod, i.e. the quotient ring (R/mathfrak {m}^i) is not Golod. Complementary to a 2014 result by Rossi and ?ega, we prove that for a generic artinian Gorenstein local ring with (mathfrak {m}^4=0ne mathfrak {m}^3), the quotient (R/mathfrak {m}^3) is not Golod. This is provided that (mathfrak {m}) is minimally generated by at least 3 elements. Indeed, we show that if (mathfrak {m}) is 2-generated, then every power (mathfrak {m}^ine 0) is Golod.