On the problem of Pillai with Tribonacci numbers and powers of 3

Let $ (T_{n})_{n\geq 0} $ be the sequence of Tribonacci numbers defined by $ T_0=0 $, $ T_1 = T_2=1$, and $ T_{n+3}=T_{n+2}+ T_{n+1} +T_n$ for all $ n\geq 0 $. In this note, we find all integers $ c $ admitting at least two representations as a difference between a tribonacci number and a power of $ 3 $.