Matrices and Determinants: JEE Main 2023 Mathematics question

Let $\mathrm{S}$ be the set of values of $\lambda$, for which the system of equations $6 \lambda x-3 y+3 z=4 \lambda^{2}$, $2 x+6 \lambda y+4 z=1$, $3 x+2 y+3 \lambda z=\lambda$ has no solution. Then 12 \sum_\limits{i \in S}|\lambda| is equal to ___________.