Go, (削除) 217 (削除ここまで) 216 bytes

package g;import("strconv";"strings";"os");var(
d=make(map[int]int)
a=strconv.Itoa)
func G(L int){k,i:=0,0;for;i<=L;i++{s:=a(i);k=0;for d[k]>0||strings.ContainsAny(a(k),s){k++;}
d[k]=1;}
os.Stdout.WriteString(a(k));}

Alternate version (program instead of a package): Try it online!

Improvements: removed space after outer for by using multiple assignment for i,k

Go, (削除) 217 (削除ここまで) 205 bytes

package g;import("fmt";"strconv";"strings");var(
d=make(map[int]int)
a=strconv.Itoa)
func G(L int){k,i:=0,0;for;i<=L;i++{s:=a(i);k=0;for d[k]>0||strings.ContainsAny(a(k),s){k++;}
d[k]=1;}
fmt.Print(a(k));}

Alternate version (program instead of a package): Try it online!

Improvements:

• removed space after outer for by using multiple assignment for i,k
• importing "fmt"; + fmt.Print is shorter than os.Stdout.WriteString (holdover from package main when os.Args was needed)

Go, 217 bytes

package g;import("strconv";"strings";"os");var(
d=make(map[int]int)
a=strconv.Itoa)
func G(L int){k:=0;for i:=0;i<=L;i++{s:=a(i);k=0;for d[k]>0||strings.ContainsAny(a(k),s){k++;}
d[k]=1;}
os.Stdout.WriteString(a(k));}

Alternate version (program instead of a package): Try it online!

Go, (削除) 217 (削除ここまで) 216 bytes

package g;import("strconv";"strings";"os");var(
d=make(map[int]int)
a=strconv.Itoa)
func G(L int){k,i:=0,0;for;i<=L;i++{s:=a(i);k=0;for d[k]>0||strings.ContainsAny(a(k),s){k++;}
d[k]=1;}
os.Stdout.WriteString(a(k));}

Alternate version (program instead of a package): Try it online!

Improvements: removed space after outer for by using multiple assignment for i,k