In Sally's Paper stretched artinian local ring is defined as :

Let $(R, \mathfrak{m})$ be an Artin local ring of length $\lambda.$ If $\nu$ is the embedding dimension of $R$, that is, $\nu$ is the number of elements in a minimal basis of $\mathfrak{m}$, then $\mathfrak{m}^{\lambda-\nu+1} = 0.$ We will say that $R$ is stretched if $\lambda - \nu$ is the least integer $i$ such that $\mathfrak{m}^{i+1} = 0.$ If $R$ is not a field, $R$ is stretched if and only if $\mathfrak{m}^2$ is principal ideal.

$\textbf{I am thinking how to construct some examples of stretched artinian local ring}.$

$\textbf{It will be better if could get those with $\lambda \neq \nu$ and $\mathfrak{m}^3 \neq 0$}.$

Any help is highly appreciated.