Let d≡2(mod4) be a square-free integer such that x2- dy2= – 1 and x2- dy2= 6 are solvable in integers. We prove the existence of infinitely many quadruples in Z[d] with the property D(n) when n∈{(4m+1)+4kd,(4m+1)+(4k+2)d,(4m+3)+4kd,(4m+3)+(4k+2)d,(4m+2)+(4k+2)d} for m, k∈ Z. As a consequence, we provide few counter examples to Conjecture 1 of Franušić and Jadrijević [Math. Slovaca 69, 1263–1278 (2019)].