lee weight for (u,u + v)-construction of codes over z4

For a linear code $c$ of length $n$ over $z_4$‎, ‎the lee support weight of $c$‎, ‎denoted by $wt_l(c)$‎, ‎is the sum of lee weights of all columns of $a(c)$, $a(c)$ is $|c| times n$ array of all codewords in $c$‎. ‎## for $1 leq r leq rank(c)$‎, ‎the $r$-th generalized lee weight with respect to rank (glwr) for $c$‎, ‎denoted by $d_r^l(c)$‎, ‎is defined as ‎begin{equation*} ‎‎‎‎‎d_r^l(c)=minlbrace wt_l(d); d text{ is a } z_4-text{submodule of c}, rank(d)=rrbrace‎‎.‎‎‎ ‎end{equation*}‎‎‎‎‎‎ ‎‎ ‎let $c_i, i=1,2$ be codes over $z_4$ ‎and ‎‎$‎‎c$ ‎denote‎ ‎‎$(u, u+v)‎$‎‎‎-construction of them. ##in this paper, we obtained $d_1^l(c)$ in terms of $d_1^l(c_1),d_1^l(c_2)$ ‎and ‎we‎ generally obtained an upper bound for $d_r^l(c)$ for all $r‎$‎‎, ‎$1 leq r leq rank(c)$‎.## we found a relationship between ‎$‎‎wt_lx‎‎$‎, ‎$wt_ly‎$ ‎and ‎$wt_l(x+y)‎‎$‎‎‎‎‎, for any ‎$‎‎x, y ‎‎in ‎z_4^n $and we showed that lee support weight is invariant un‎‎der multiplication by 3