  In terms of the creative microscoping method recently introduced by Guo and
Zudilin [Adv. Math. 346 (2019), 329--358], we find a $q$-supercongruence with
four parameters modulo $\Phi_n(q)(1-aq^n)(a-q^n)$, where $\Phi_n(q)$ denotes
the $n$-th cyclotomic polynomial in $q$. Then we empoly it and the Chinese
remainder theorem for coprime polynomials to derive a $q$-supercongruence with
two parameters modulo $[n]\Phi_n(q)^3$, where $[n]=(1-q^n)/(1-q)$ is the
$q$-integer.
